Finite Group Databasebeta

← #33092646

Subgroups — #33092646

Order 18688.

1010 conjugacy classes of subgroups.

The subgroup lattice has 694 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988831C211yesmaximal, characteristic
2C2×C4×#11924016C211yesmaximal, characteristic, complemented
3C2×#17988543C211yesmaximal, characteristic, complemented
4#22612613C211yesmaximal, characteristic, complemented
5#22610811C211yesmaximal, characteristic, complemented
6#22610666C211yesmaximal, characteristic, complemented
7#22610617C211yesmaximal, characteristic, complemented
8#22610606C211yesmaximal, characteristic, complemented
9#22610360C211yesmaximal, characteristic
10#22610352C211yesmaximal, characteristic, complemented
11#22609962C211yesmaximal, characteristic, complemented
12C4×#14556524C211yesmaximal, characteristic, complemented
13#22609764C211yesmaximal, characteristic, complemented
14#22609756C211yesmaximal, characteristic, complemented
15C73×#2324C211yesmaximal, characteristic
16C22×#11924016C2211yescharacteristic
17C22×#11924012C2211yescharacteristic
18C23×#10596831C2211yescharacteristic
19C2×#14556570C2211yescharacteristic
20C2×C4×Dic146C2211yescharacteristic
21#17988831C418yescomplemented
22C4×#11924016—24no—
23C2×#14556524C2211yescharacteristic
24C2×#14556524C2211yescharacteristic
25C2×#14556522C2211yescharacteristic
26C2×#14556514C2211yescharacteristic
27C2×#14556514C2211yescharacteristic
28C2×#14556514C2211yescharacteristic
29C2×#14556512C2211yescharacteristic
30C2×#14556512C2211yescharacteristic
31C2×#14556512C2211yescharacteristic
32#17988543—24no—
33C2×#14556502C2211yescharacteristic
34C2×#14556502C2211yescharacteristic
35C2×C4×#10596831C2211yescharacteristic
36C2×C4×#10596831C2211yescharacteristic
37#17988493C2211yescharacteristic
38#17988485C2211yescharacteristic
39#17988482—21no—
40#17988481—21no—
41#17988475—21no—
42#17988468—21no—
43#17988447C2211yescharacteristic
44C4×C4⋊Dic73C2211yescharacteristic
45#17988349C2211yescharacteristic
46#17988349C2211yescharacteristic
47#17988349C2211yescharacteristic
48#17988349C2211yescharacteristic
49#17988349C2211yescharacteristic
50#17988349C2211yescharacteristic
51C2×#121×C73C2211yescharacteristic
52C2×C4×D4×C73C2211yescharacteristic
53C2×#117×C73C2211yescharacteristic
54#390×C73—21no—
55#390×C73C2211yescharacteristic
56#389×C73C2211yescharacteristic
57#388×C73—21no—
58#386×C73—21no—
59#385×C73—21no—
60#380×C73C2211yescharacteristic
61C4×C4⋊C4×C73C2211yescharacteristic
62C22×Dic146C2311yescharacteristic
63C2×#11924016—22no—
64C2×#11924016—22no—
65C2×#11924016C2×C414yes—
66C2×#11924012—22no—
67C2×#11924012—22no—
68C2×#11924012C2×C414yescomplemented
69C22×#10596831—22no—
70C22×#10596831—22no—
71C22×#10596831—22no—
72C22×#10596831C2311yescharacteristic
73C22×#10596831C2311yescharacteristic
74C22×#10596831C2311yescharacteristic
75C22×#10596831C2311yescharacteristic
76#14556570—22no—
77#14556570C2×C414yescomplemented
78C4×Dic146—22no—
79C4×Dic146—22no—
80C2×C4⋊Dic73C2311yescharacteristic
81C2×C4⋊Dic73C2311yescharacteristic
82C2×C4⋊Dic73C2311yescharacteristic
83C2×#11924007—21no—
84C2×#11924007—21no—
85C2×#11924007—21no—
86C2×C22⋊Dic73—21no—
87C2×C22⋊Dic73—21no—
88C2×C4×Dic73—21no—
89C2×C4×Dic73—21no—
90#14556524—22no—
91#14556524C2×C414yescomplemented
92#14556522—22no—
93#14556514—22no—
94#14556514—22no—
95#14556514C2×C414yescomplemented
96#14556512—22no—
97#14556512—22no—
98#14556512C2×C414yes—
99#14556502—22no—
100#14556502—22no—
101C4×#10596831—22no—
102C4×#10596831D414yescomplemented
103#14556498—21no—
104#14556498—21no—
105#14556498—21no—
106#14556498—21no—
107#14556498—21no—
108C22×D4×C73—21no—
109C22×D4×C73C2311yescharacteristic
110C23×C4×C73—21no—
111C23×C4×C73C2311yescharacteristic
112#121×C73—22no—
113#121×C73C2×C414yes—
114C4×D4×C73—22no—
115C4×D4×C73—22no—
116#117×C73—22no—
117#117×C73—22no—
118C2×C4⋊C4×C73—21no—
119C2×C4⋊C4×C73D411yescharacteristic
120C2×C4⋊C4×C73D411yescharacteristic
121C2×C4⋊C4×C73C2311yescharacteristic
122C2×C4⋊C4×C73C2311yescharacteristic
123C2×C4⋊C4×C73C2311yescharacteristic
124C2×C22⋊C4×C73—21no—
125C2×C22⋊C4×C73—21no—
126C2×C22⋊C4×C73—21no—
127C2×C22⋊C4×C73—21no—
128C2×C22⋊C4×C73—21no—
129C2×C22⋊C4×C73D411yescharacteristic
130C2×C22⋊C4×C73D411yescharacteristic
131C2×C42×C73—21no—
132C2×C42×C73C2311yescharacteristic
133C2×C42×C73C2311yescharacteristic
134#95×C73—21no—
135#95×C73—21no—
136#95×C73—21no—
137C2×Dic146—21no—
138C2×Dic146—21no—
139C2×Dic146—21no—
140C2×Dic146—21no—
141C2×Dic146—21no—
142C2×Dic146C22×C412yes—
143C22×Dic73—21no—
144C22×Dic73—21no—
145C22×Dic73—21no—
146C22×Dic73—21no—
147#11924016—28no—
148#11924012—28no—
149C2×#10596831—28no—
150C2×#10596831—21no—
151C2×#10596831—21no—
152C2×#10596831—21no—
153C2×#10596831—21no—
154C2×#10596831—21no—
155C2×#10596831—21no—
156C2×#10596831C22×C412yes—
157C2×#10596831C22×C412yes—
158C2×#10596831C2×D412yes—
159C2×#10596831C2×D412yes—
160C2×#10596831#4112yes—
161C2×#10596831#4112yes—
162C4⋊Dic73—21no—
163C4⋊Dic73—21no—
164C4⋊Dic73—21no—
165C4⋊Dic73—21no—
166C4⋊Dic73—21no—
167C4⋊Dic73C22×C412yes—
168#11924007—24no—
169#11924007—42no—
170#11924007—81no—
171C22⋊Dic73—24no—
172C22⋊Dic73—81no—
173C4×Dic73—42no—
174C4×Dic73—81no—
175C24×C73—21no—
176C24×C73C2×D411yescharacteristic
177C2×D4×C73—24no—
178C2×D4×C73—21no—
179C2×D4×C73—21no—
180C2×D4×C73—21no—
181C2×D4×C73—21no—
182C2×D4×C73—21no—
183C2×D4×C73—81no—
184C2×D4×C73—81no—
185C2×D4×C73C22×C412yes—
186C22×C4×C73—21no—
187C22×C4×C73—21no—
188C22×C4×C73—21no—
189C22×C4×C73—21no—
190C22×C4×C73—21no—
191C22×C4×C73—21no—
192C22×C4×C73—21no—
193C22×C4×C73—42no—
194C22×C4×C73—81no—
195C22×C4×C73—81no—
196C22×C4×C73C22×C412yes—
197C22×C4×C73C2×D411yescharacteristic
198C22×C4×C73C2×D411yescharacteristic
199C22×C4×C73C2×D411yescharacteristic
200C22×C4×C73C2×D411yescharacteristic
201C22×C4×C73C2×D411yescharacteristic
202C22×C4×C73#4112yes—
203C22×C4×C73C2411yescharacteristic
204C4⋊C4×C73—22no—
205C4⋊C4×C73—22no—
206C4⋊C4×C73—21no—
207C4⋊C4×C73—21no—
208C4⋊C4×C73—21no—
209C4⋊C4×C73—21no—
210C4⋊C4×C73—21no—
211C4⋊C4×C73—81no—
212C4⋊C4×C73C22×C412yes—
213C22⋊C4×C73—24no—
214C22⋊C4×C73—22no—
215C22⋊C4×C73—22no—
216C22⋊C4×C73—42no—
217C22⋊C4×C73—81no—
218C22⋊C4×C73—81no—
219C22⋊C4×C73—81no—
220C42×C73—21no—
221C42×C73—21no—
222C42×C73—81no—
223C42×C73C2×D412yes—
224C42×C73#4112yes—
225C23×C73—21no—
226C23×C73—21no—
227C23×C73—21no—
228C23×C73—21no—
229C23×C73—21no—
230C23×C73—21no—
231C23×C73—22no—
232C23×C73—41no—
233C23×C73—41no—
234C23×C73—41no—
235C23×C73—41no—
236C23×C73—41no—
237C23×C73—41no—
238C23×C73C4×D412yes—
239C23×C73C22×D411yescharacteristic
240D4×C73—22no—
241D4×C73—22no—
242D4×C73—41no—
243D4×C73—41no—
244D4×C73—84no—
245C2×C4×C73—21no—
246C2×C4×C73—21no—
247C2×C4×C73—21no—
248C2×C4×C73—21no—
249C2×C4×C73—21no—
250C2×C4×C73—21no—
251C2×C4×C73—22no—
252C2×C4×C73—22no—
253C2×C4×C73—22no—
254C2×C4×C73—22no—
255C2×C4×C73—22no—
256C2×C4×C73—21no—
257C2×C4×C73—21no—
258C2×C4×C73—21no—
259C2×C4×C73—21no—
260C2×C4×C73—21no—
261C2×C4×C73—21no—
262C2×C4×C73—41no—
263C2×C4×C73—41no—
264C2×C4×C73—41no—
265C2×C4×C73—41no—
266C2×C4×C73—41no—
267C2×C4×C73—41no—
268C2×C4×C73—41no—
269C2×C4×C73—41no—
270C2×C4×C73—84no—
271C2×C4×C73C4×D412yes—
272C2×C4×C73#12112yes—
273C2×C4×C73#12112yes—
274C2×C4×C73C23×C411yescharacteristic
275C2×C4×C73C22×D411yescharacteristic
276C2×C4×C73C2×#4111yescharacteristic
277C2×C4×C73C2×#4111yescharacteristic
278C2×C4×C73C2×#4111yescharacteristic
279C2×C4×C73C2×#4111yescharacteristic
280C2×Dic73—22no—
281C2×Dic73—22no—
282C2×Dic73—41no—
283C2×Dic73—41no—
284C2×Dic73—41no—
285C2×Dic73—41no—
286C2×Dic73—41no—
287C2×Dic73—41no—
288C2×Dic73—41no—
289C2×Dic73—41no—
290C2×Dic73—41no—
291C2×Dic73—41no—
292Dic146—22no—
293Dic146—22no—
294Dic146—41no—
295Dic146—41no—
296#10596831—22no—
297#10596831—22no—
298#10596831—22no—
299#10596831C4×D414yes—
300C22×C73—22no—
301C22×C73—22no—
302C22×C73—22no—
303C22×C73—41no—
304C22×C73—41no—
305C22×C73—41no—
306C22×C73—41no—
307C22×C73—42no—
308C22×C73—42no—
309C22×C73—42no—
310C22×C73—81no—
311C22×C73—81no—
312C22×C73—81no—
313C22×C73—81no—
314C22×C73C2×C4×D411yescharacteristic
315C22×C73C2×#12111yescharacteristic
316C22×C73#53211yescharacteristic
317C22×C73#57611yescharacteristic
318C22×C73#57711yescharacteristic
319C22×C73#57711yescharacteristic
320C22×C73#57811yescharacteristic
321C4×C73—22no—
322C4×C73—22no—
323C4×C73—22no—
324C4×C73—42no—
325C4×C73—41no—
326C4×C73—41no—
327C4×C73—81no—
328C4×C73—81no—
329C4×C73C2×C4×D411yescharacteristic
330C4×C73C4×#4111yescharacteristic
331C4×C73#52511yescharacteristic
332C4×C73#52911yescharacteristic
333Dic73—42no—
334Dic73—42no—
335Dic73—81no—
336Dic73—81no—
337#21535—731nomaximal, Sylow
338C2×C73—42no—
339C2×C73—82no—
340C2×C73C4×#12111yescharacteristic
341C2×C73#294611yescharacteristic
342C2×C73#294711yescharacteristic
343C2×C73#305711yescharacteristic
344C2×C73#306111yescharacteristic
345C2×C73#317811yescharacteristic
346C2×C73#317911yescharacteristic
347C2×#468—731no—
348C2×C4×SD16—731no—
349C2×#405—731no—
350#2324D7311yescharacteristic
351#2323—731no—
352#1973—731no—
353#1943—731no—
354#1934—731no—
355#1933—731no—
356#1893—731no—
357#1892—731no—
358#1809—731no—
359C4×#107—731no—
360#1763—731no—
361#1762—731no—
362C73#2153511yescharacteristic, complemented, Sylow
363C22×SD16—731no—
364C22×M16—731no—
365C23×C8—731no—
366C2×C22⋊Q8—731no—
367C2×#121C2×D7311yescharacteristic
368C2×C4×Q8—731no—
369C2×C4×D4C2×D7311yescharacteristic
370C2×#117C2×D7311yescharacteristic
371#468—738no—
372C4×SD16—1464no—
373C2×#107—731no—
374C2×#107—731no—
375C2×#106—731no—
376C2×#103—731no—
377C2×#103—731no—
378C2×#103—731no—
379C2×#102—731no—
380C2×#102—731no—
381C2×#102—731no—
382#405—1464no—
383C2×#97—731no—
384C2×#97—731no—
385C2×C4×C8—731no—
386C2×C4×C8—731no—
387#391—731no—
388#390—21no—
389#390C2×D7311yescharacteristic
390#389—731no—
391#389—1461no—
392#389C2×D7311yescharacteristic
393#388—21no—
394#388—1461no—
395#388—1461no—
396#387—1461no—
397#386—21no—
398#385—21no—
399#380—731no—
400#380C2×D7311yescharacteristic
401C4×C4⋊C4—731no—
402C4×C4⋊C4C2×D7311yescharacteristic
403#340—731no—
404#340—731no—
405#340—731no—
406#340—731no—
407#340—731no—
408#340—731no—
409C22×Q8—731no—
410C22×D4—21no—
411C22×D4C22×D7311yescharacteristic
412C23×C4—21no—
413C23×C4C22×D7311yescharacteristic
414C2×SD16—734no—
415C2×SD16—1462no—
416C2×SD16—1462no—
417C2×M16—734no—
418C2×M16—1462no—
419C2×M16—1462no—
420C22×C8—731no—
421C22×C8—731no—
422C22×C8—731no—
423C22×C8—731no—
424C22×C8—1462no—
425C22×C8—1462no—
426C22×C8—1462no—
427C22⋊Q8—734no—
428C22⋊Q8—1462no—
429#121—22no—
430#121C4×D7314yes—
431C4×Q8—1462no—
432C4×Q8—1462no—
433C4×D4—22no—
434C4×D4—22no—
435#117—22no—
436#117—22no—
437C2×C4⋊C4—21no—
438C2×C4⋊C4—731no—
439C2×C4⋊C4—731no—
440C2×C4⋊C4—731no—
441C2×C4⋊C4—1461no—
442C2×C4⋊C4—1461no—
443C2×C4⋊C4—1461no—
444C2×C4⋊C4C22⋊D7311yescharacteristic
445C2×C4⋊C4C22⋊D7311yescharacteristic
446C2×C4⋊C4C22×D7311yescharacteristic
447C2×C4⋊C4C22×D7311yescharacteristic
448C2×C4⋊C4C22×D7311yescharacteristic
449C2×C22⋊C4—21no—
450C2×C22⋊C4—21no—
451C2×C22⋊C4—21no—
452C2×C22⋊C4—21no—
453C2×C22⋊C4—21no—
454C2×C22⋊C4—1461no—
455C2×C22⋊C4—1461no—
456C2×C22⋊C4C22⋊D7311yescharacteristic
457C2×C22⋊C4C22⋊D7311yescharacteristic
458C2×C42—21no—
459C2×C42—1461no—
460C2×C42—1461no—
461C2×C42C22×D7311yescharacteristic
462C2×C42C22×D7311yescharacteristic
463#107—734no—
464#107—1462no—
465#106—1462no—
466#103—734no—
467#103—1462no—
468#103—1462no—
469#102—734no—
470#102—1462no—
471#102—1462no—
472#97—1462no—
473#97—1462no—
474C4×C8—734no—
475C4×C8—1462no—
476#95—21no—
477#95—21no—
478#95—21no—
479#95—1461no—
480#95—1461no—
481#95—1461no—
482#95—1461no—
483#95—1461no—
484C24—21no—
485C24C2×C22⋊D7311yescharacteristic
486C2×Q8—732no—
487C2×Q8—1461no—
488C2×Q8—1461no—
489C2×Q8—1461no—
490C2×Q8—1461no—
491C2×Q8—1461no—
492C2×D4—24no—
493C2×D4—21no—
494C2×D4—21no—
495C2×D4—21no—
496C2×D4—21no—
497C2×D4—21no—
498C2×D4—81no—
499C2×D4—81no—
500C2×D4C2×C4×D7312yes—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—42no—
509C22×C4—81no—
510C22×C4—81no—
511C22×C4—1461no—
512C22×C4—1461no—
513C22×C4—1461no—
514C22×C4—1461no—
515C22×C4C2×C4×D7312yes—
516C22×C4C2×C22⋊D7311yescharacteristic
517C22×C4C2×C22⋊D7311yescharacteristic
518C22×C4C2×C22⋊D7311yescharacteristic
519C22×C4C2×C22⋊D7311yescharacteristic
520C22×C4C2×C22⋊D7311yescharacteristic
521C22×C4#1192402812yes—
522C22×C4C23×D7311yescharacteristic
523SD16—1468no—
524M16—1468no—
525C2×C8—732no—
526C2×C8—732no—
527C2×C8—732no—
528C2×C8—732no—
529C2×C8—732no—
530C2×C8—732no—
531C2×C8—1468no—
532C2×C8—1461no—
533C2×C8—1461no—
534C2×C8—1461no—
535C2×C8—1461no—
536C2×C8—1461no—
537C2×C8—1461no—
538C4⋊C4—22no—
539C4⋊C4—22no—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—81no—
546C4⋊C4—2922no—
547C4⋊C4—5841no—
548C4⋊C4—732no—
549C4⋊C4—1461no—
550C4⋊C4—1461no—
551C4⋊C4—1461no—
552C4⋊C4—1461no—
553C4⋊C4—1464no—
554C4⋊C4—1461no—
555C4⋊C4C2×C4×D7312yes—
556C22⋊C4—24no—
557C22⋊C4—22no—
558C22⋊C4—22no—
559C22⋊C4—42no—
560C22⋊C4—81no—
561C22⋊C4—81no—
562C22⋊C4—81no—
563C22⋊C4—5841no—
564C22⋊C4—1464no—
565C42—21no—
566C42—21no—
567C42—81no—
568C42—2922no—
569C42—5841no—
570C42D4×D7312yes—
571C42#1192402712yes—
572C23—21no—
573C23—21no—
574C23—21no—
575C23—21no—
576C23—21no—
577C23—21no—
578C23—22no—
579C23—41no—
580C23—41no—
581C23—41no—
582C23—41no—
583C23—41no—
584C23—41no—
585C23C4×C22⋊D7312yes—
586C23C22×C22⋊D7311yescharacteristic
587Q8—2921no—
588Q8—2921no—
589Q8—1462no—
590Q8—1462no—
591D4—22no—
592D4—22no—
593D4—41no—
594D4—41no—
595D4—84no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—22no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—22no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—84no—
622C2×C4—2921no—
623C2×C4—2921no—
624C2×C4—2921no—
625C2×C4—2921no—
626C2×C4—2921no—
627C2×C4—2921no—
628C2×C4—2921no—
629C2×C4—2921no—
630C2×C4—2921no—
631C2×C4—2921no—
632C2×C4—1462no—
633C2×C4—1462no—
634C2×C4C4×C22⋊D7312yes—
635C2×C4#1455656312yes—
636C2×C4#1455656312yes—
637C2×C4C22×C4×D7311yescharacteristic
638C2×C4C2×D4×D7311yescharacteristic
639C2×C4#41×D7311yescharacteristic
640C2×C4#41×D7311yescharacteristic
641C2×C4C2×#1192402711yescharacteristic
642C2×C4C2×#1192402811yescharacteristic
643C8—734no—
644C8—1462no—
645C8—1462no—
646C8—1462no—
647C22—22no—
648C22—22no—
649C22—22no—
650C22—41no—
651C22—41no—
652C22—41no—
653C22—41no—
654C22—42no—
655C22—42no—
656C22—42no—
657C22—81no—
658C22—81no—
659C22—81no—
660C22—81no—
661C22C2×C4×C22⋊D7311yescharacteristic
662C22C2×#1455656311yescharacteristic
663C22#1798913311yescharacteristic
664C22#1798939011yescharacteristic
665C22#1798939811yescharacteristic
666C22#1798939811yescharacteristic
667C22#1798940211yescharacteristic
668C4—22no—
669C4—22no—
670C4—22no—
671C4—42no—
672C4—41no—
673C4—41no—
674C4—81no—
675C4—81no—
676C4—2922no—
677C4—2922no—
678C4—5841no—
679C4—5841no—
680C4C4×D4×D7311yescharacteristic
681C4C4×#1192402711yescharacteristic
682C4#1798909611yescharacteristic
683C4#1798911711yescharacteristic
684C2—42no—
685C2—82no—
686C2C4×#1455656311yescharacteristic
687C2#2261876311yescharacteristic
688C2#2261877011yescharacteristic
689C2#2261956711yescharacteristic
690C2#2261959811yescharacteristic
691C2#2262059311yescharacteristic
692C2#2262061611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D73
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC73×#2324C2
socleC23×C73C22×D4
prime radicalC2×#121×C73C22
cosocleC22×C4×C73C24
hypercenter#2324D73
hypocenterC73#21535
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2324

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×C4×#11924016C2semidirect
3. C2×#17988543C2semidirect
4. #22612613C2semidirect
5. #22610811C2semidirect
6. #22610666C2semidirect
7. #22610617C2semidirect
8. #22610606C2semidirect
10. #22610352C2semidirect
11. #22609962C2semidirect
12. C4×#14556524C2semidirect
13. #22609764C2semidirect
14. #22609756C2semidirect
21. #17988831C4semidirect
68. C2×#11924012C2×C4semidirect
77. #14556570C2×C4semidirect
91. #14556524C2×C4semidirect
95. #14556514C2×C4semidirect
102. C4×#10596831D4semidirect
362. C73#21535semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#179888312
C2×C4×#119240162
C2×#179885432
#226126132
#226108112
#226106662
#226106172
#226106062
#226103602
#226103522
#226099622
C4×#145565242
#226097642
#226097562
C73×#23242
#2153573