Finite Group Databasebeta

← #33007697

Subgroups — #33007697

Order 18688.

2118 conjugacy classes of subgroups.

The subgroup lattice has 710 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556548C211yesmaximal, characteristic
2C2×C4×#11924007C211yesmaximal, characteristic, complemented
3C2×C4×C4⋊Dic73C211yesmaximal, characteristic, complemented
4C2×C4×#11924005C211yesmaximal, characteristic
5C2×C4×#11924005C211yesmaximal, characteristic
6#22608195C212yesmaximal, complemented
7#22608186C212yesmaximal, complemented
8#22608177C212yesmaximal
9#22608175C212yesmaximal
10C4×#14556498C211yesmaximal, characteristic, complemented
11C4×#95×C73C211yesmaximal, characteristic, complemented
12C23×C4×D73C2211yescharacteristic
13C2×#14556548—24no—
14C2×#14556548—24no—
15C2×#14556548—24no—
16C22×C4⋊Dic73C2212yes—
17C22×#11924007C2212yes—
18C22×#11924007C2212yes—
19C22×#11924005C2212yes—
20C22×#11924005C2212yes—
21C22×#11924005C2211yescharacteristic
22C22×#11924005C2211yescharacteristic
23C22×C4×Dic73C2211yescharacteristic
24C22×C4×Dic73C2211yescharacteristic
25C22×C4×Dic73C2211yescharacteristic
26C4×#11924007—24no—
27C4×C4⋊Dic73—24no—
28C4×#11924005—24no—
29C4×#11924005C418yescomplemented
30C2×#14556498C2212yes—
31C2×#14556498C2212yes—
32C2×#14556498C2212yes—
33C2×#14556498C2212yes—
34C2×#14556498C2212yes—
35C2×#14556498C2211yescharacteristic
36C2×#14556498C2211yescharacteristic
37C22×C42×C73C2211yescharacteristic
38C22×C42×C73C2211yescharacteristic
39C22×C42×C73C2211yescharacteristic
40C2×#95×C73C2212yes—
41C2×#95×C73C2212yes—
42C24×D73C2311yescharacteristic
43C23×Dic73C2311yescharacteristic
44C23×Dic73C2312yes—
45C23×Dic73C2312yes—
46C23×Dic73C2311yescharacteristic
47C23×Dic73C2311yescharacteristic
48C22×C4×D73—22no—
49C22×C4×D73—22no—
50C22×C4×D73—22no—
51C22×C4×D73—22no—
52C22×C4×D73C2×C414yes—
53C22×C4×D73D414yes—
54C22×C4×D73Q814yes—
55#14556548—232no—
56C2×C4⋊Dic73—24no—
57C2×C4⋊Dic73—24no—
58C2×C4⋊Dic73—24no—
59C2×#11924007—24no—
60C2×#11924007—24no—
61C2×#11924007—24no—
62C2×#11924007—24no—
63C2×#11924007—24no—
64C2×#11924007—24no—
65C2×#11924005—24no—
66C2×#11924005—24no—
67C2×#11924005—24no—
68C2×#11924005—24no—
69C2×#11924005—24no—
70C2×#11924005—24no—
71C2×#11924005—24no—
72C2×#11924005—24no—
73C2×#11924005C2×C414yes—
74C2×#11924005C2×C414yes—
75C2×C4×Dic73—22no—
76C2×C4×Dic73—22no—
77C2×C4×Dic73—22no—
78C2×C4×Dic73—22no—
79C2×C4×Dic73—22no—
80C2×C4×Dic73—22no—
81C2×C4×Dic73—22no—
82C2×C4×Dic73C2×C414yes—
83C2×C4×Dic73D414yes—
84#14556498—24no—
85#14556498—24no—
86#14556498—24no—
87#14556498—24no—
88#14556498—24no—
89#14556498C2×C414yes—
90#14556498C2×C414yes—
91C23×C4×C73C2311yescharacteristic
92C23×C4×C73C2312yes—
93C23×C4×C73C2312yes—
94C23×C4×C73C2311yescharacteristic
95C23×C4×C73C2311yescharacteristic
96C2×C42×C73—22no—
97C2×C42×C73—22no—
98C2×C42×C73—22no—
99C2×C42×C73—22no—
100C2×C42×C73—22no—
101C2×C42×C73—22no—
102C2×C42×C73—22no—
103C2×C42×C73C2×C414yes—
104C2×C42×C73D414yes—
105#95×C73—24no—
106#95×C73—24no—
107C23×D73—21no—
108C23×D73—21no—
109C23×D73—22no—
110C23×D73—22no—
111C23×D73—22no—
112C23×D73—22no—
113C23×D73—21no—
114C23×D73—21no—
115C23×D73C22×C412yes—
116C23×D73C2×D412yes—
117C23×D73C2×Q812yes—
118C22×Dic73—21no—
119C22×Dic73—21no—
120C22×Dic73—21no—
121C22×Dic73—21no—
122C22×Dic73—22no—
123C22×Dic73—21no—
124C22×Dic73—21no—
125C22×Dic73—21no—
126C22×Dic73—22no—
127C22×Dic73—22no—
128C22×Dic73—22no—
129C22×Dic73—22no—
130C22×Dic73—22no—
131C22×Dic73—22no—
132C22×Dic73—22no—
133C22×Dic73—22no—
134C22×Dic73—21no—
135C22×Dic73—22no—
136C22×Dic73—22no—
137C22×Dic73—22no—
138C22×Dic73—22no—
139C22×Dic73—22no—
140C22×Dic73—22no—
141C22×Dic73C22×C412yes—
142C22×Dic73C22×C412yes—
143C22×Dic73C22×C412yes—
144C22×Dic73C2×D414yes—
145C22×Dic73C2×D412yes—
146C22×Dic73C2×Q812yes—
147C22×Dic73#4114yes—
148C22×Dic73#4114yes—
149C2×C4×D73—28no—
150C2×C4×D73—28no—
151C2×C4×D73—28no—
152C2×C4×D73—28no—
153C2×C4×D73—28no—
154C2×C4×D73—28no—
155C2×C4×D73C4⋊C4116yescomplemented
156C4⋊Dic73—216no—
157#11924007—216no—
158#11924007—216no—
159#11924005—216no—
160#11924005—216no—
161#11924005—28no—
162#11924005—28no—
163C4×Dic73—28no—
164C4×Dic73—28no—
165C4×Dic73—44no—
166C24×C73C2411yescharacteristic
167C22×C4×C73—21no—
168C22×C4×C73—21no—
169C22×C4×C73—22no—
170C22×C4×C73—21no—
171C22×C4×C73—22no—
172C22×C4×C73—22no—
173C22×C4×C73—22no—
174C22×C4×C73—22no—
175C22×C4×C73—22no—
176C22×C4×C73—22no—
177C22×C4×C73—22no—
178C22×C4×C73—21no—
179C22×C4×C73—22no—
180C22×C4×C73—22no—
181C22×C4×C73—22no—
182C22×C4×C73—22no—
183C22×C4×C73—22no—
184C22×C4×C73—22no—
185C22×C4×C73—22no—
186C22×C4×C73C22×C412yes—
187C22×C4×C73C22×C412yes—
188C22×C4×C73C22×C412yes—
189C22×C4×C73C2×D412yes—
190C22×C4×C73C2×D412yes—
191C22×C4×C73C2×D414yes—
192C22×C4×C73C2×D412yes—
193C22×C4×C73C2×Q812yes—
194C22×C4×C73#4112yes—
195C22×C4×C73#4114yes—
196C22×C4×C73#4114yes—
197C22×C4×C73#4112yes—
198C42×C73—28no—
199C42×C73—28no—
200C42×C73—44no—
201C23×C73C23×C411yescharacteristic
202C23×C73C22×D411yescharacteristic
203C23×C73C22×D411yescharacteristic
204C23×C73C22×D411yescharacteristic
205C23×C73C22×Q811yescharacteristic
206C23×C73C2×#4112yes—
207C23×C73C2×#4112yes—
208C23×C73C2×#4111yescharacteristic
209C23×C73C2×#4112yes—
210C23×C73C2×#4111yescharacteristic
211C23×C73C2×#4112yes—
212C22×D73—22no—
213C22×D73—22no—
214C22×D73—22no—
215C22×D73—22no—
216C22×D73—22no—
217C22×D73—22no—
218C22×D73—22no—
219C22×D73—22no—
220C22×D73—22no—
221C22×D73—22no—
222C22×D73—24no—
223C22×D73—24no—
224C22×D73—24no—
225C22×D73—24no—
226C22×D73—42no—
227C22×D73—42no—
228C22×D73—42no—
229C22×D73—42no—
230C22×D73—42no—
231C22×D73—42no—
232C22×D73—42no—
233C22×D73—42no—
234C22×D73C2×C4⋊C414yes—
235C2×C4×C73—22no—
236C2×C4×C73—22no—
237C2×C4×C73—24no—
238C2×C4×C73—24no—
239C2×C4×C73—22no—
240C2×C4×C73—22no—
241C2×C4×C73—22no—
242C2×C4×C73—24no—
243C2×C4×C73—24no—
244C2×C4×C73—24no—
245C2×C4×C73—24no—
246C2×C4×C73—24no—
247C2×C4×C73—24no—
248C2×C4×C73—42no—
249C2×C4×C73—42no—
250C2×C4×C73—42no—
251C2×C4×C73—42no—
252C2×C4×C73—42no—
253C2×C4×C73—42no—
254C2×C4×C73—42no—
255C2×C4×C73—42no—
256C2×C4×C73—42no—
257C2×C4×C73—42no—
258C2×C4×C73C2×C4⋊C414yes—
259C2×C4×C73#11714yescomplemented
260C2×C4×C73C4×D414yes—
261C2×C4×C73C4×D414yes—
262C2×C4×C73#12014yes—
263C2×C4×C73C22⋊Q814yes—
264C2×C4×C73C22⋊Q814yes—
265C2×C4×C73#12314yes—
266C2×Dic73—22no—
267C2×Dic73—22no—
268C2×Dic73—22no—
269C2×Dic73—22no—
270C2×Dic73—22no—
271C2×Dic73—22no—
272C2×Dic73—22no—
273C2×Dic73—22no—
274C2×Dic73—24no—
275C2×Dic73—24no—
276C2×Dic73—22no—
277C2×Dic73—22no—
278C2×Dic73—22no—
279C2×Dic73—24no—
280C2×Dic73—24no—
281C2×Dic73—24no—
282C2×Dic73—24no—
283C2×Dic73—24no—
284C2×Dic73—24no—
285C2×Dic73—42no—
286C2×Dic73—42no—
287C2×Dic73—42no—
288C2×Dic73—42no—
289C2×Dic73—42no—
290C2×Dic73—42no—
291C2×Dic73—42no—
292C2×Dic73—42no—
293C2×Dic73—42no—
294C2×Dic73—42no—
295C2×Dic73C2×C4⋊C414yes—
296C2×Dic73#11714yescomplemented
297C4×D73—232no—
298C22×C73C22×C4⋊C411yescharacteristic
299C22×C73C2×#11711yescharacteristic
300C22×C73C2×#11711yescharacteristic
301C22×C73C2×C4×D411yescharacteristic
302C22×C73C2×C4×D411yescharacteristic
303C22×C73C4×#4111yescharacteristic
304C22×C73C4×#4111yescharacteristic
305C22×C73C2×#12011yescharacteristic
306C22×C73C2×C22⋊Q811yescharacteristic
307C22×C73C2×C22⋊Q811yescharacteristic
308C22×C73C2×#12311yescharacteristic
309C22×C73#52512yes—
310C22×C73#52512yes—
311C22×C73#52512yes—
312C22×C73#52912yes—
313C22×C73#52912yes—
314C22×C73#52912yes—
315C22×C73#52912yes—
316C22×C73#53212yes—
317C22×C73#53212yes—
318C22×C73#53212yes—
319C22×C73#53312yes—
320C22×C73#53312yes—
321C2×D73—24no—
322C2×D73—24no—
323C2×D73—24no—
324C2×D73—44no—
325C2×D73—44no—
326C2×D73—44no—
327C2×D73—44no—
328C2×D73—42no—
329C2×D73—42no—
330C2×D73—42no—
331C2×D73—42no—
332C4×C73—24no—
333C4×C73—44no—
334C4×C73—44no—
335C4×C73—42no—
336C4×C73#38518yes—
337Dic73—24no—
338Dic73—24no—
339Dic73—44no—
340Dic73—44no—
341Dic73—42no—
342#13844—731nomaximal, Sylow
343C2×C73#228511yescharacteristic
344C2×C73C2×#38511yescharacteristic
345C2×C73#229011yescharacteristic
346C2×C73#229011yescharacteristic
347C2×C73#229311yescharacteristic
348C2×C73#229311yescharacteristic
349C2×C73#229611yescharacteristic
350C2×C73#238812yes—
351C2×C73#239512yes—
352C2×C73#239612yes—
353C2×C73#239612yes—
354D73—44no—
355C22×#117—731no—
356C2×C4×C4⋊C4—731no—
357C2×C4×C4⋊C4—731no—
358C2×C4×C22⋊C4—731no—
359C2×C4×C22⋊C4—731no—
360#1444—732no—
361#1442—732no—
362#1439—732no—
363#1439—732no—
364C4×#95—731no—
365C4×#95D7311yescharacteristic, complemented
366C73#1384411yescharacteristic, complemented, Sylow
367C24×C4—731no—
368C2×#117—1464no—
369C2×#117—1464no—
370C2×#117—1464no—
371C22×C4⋊C4—732no—
372C22×C4⋊C4—732no—
373C22×C4⋊C4—732no—
374C22×C22⋊C4—731no—
375C22×C22⋊C4—731no—
376C22×C22⋊C4—732no—
377C22×C22⋊C4—732no—
378C22×C42—731no—
379C22×C42—731no—
380C22×C42—731no—
381C22×C42C2×D7311yescharacteristic
382C22×C42C2×D7311yescharacteristic
383C22×C42C2×D7311yescharacteristic
384C4×C4⋊C4—1464no—
385C4×C4⋊C4—1464no—
386C4×C22⋊C4—738no—
387C4×C22⋊C4—1464no—
388C2×#95—731no—
389C2×#95—731no—
390C2×#95—732no—
391C2×#95—732no—
392C2×#95—732no—
393C2×#95—732no—
394C2×#95—732no—
395C2×#95C2×D7312yes—
396C2×#95C2×D7312yes—
397C25—731no—
398C23×C4—731no—
399C23×C4—731no—
400C23×C4—734no—
401C23×C4—734no—
402C23×C4—734no—
403C23×C4—732no—
404C23×C4—732no—
405C23×C4—731no—
406C23×C4—1462no—
407C23×C4—1462no—
408C23×C4—1462no—
409C23×C4—1462no—
410C23×C4C22×D7311yescharacteristic
411C23×C4C22×D7312yes—
412C23×C4C22×D7312yes—
413C23×C4C22×D7311yescharacteristic
414C23×C4C22×D7311yescharacteristic
415#117—14632no—
416C2×C4⋊C4—1464no—
417C2×C4⋊C4—1464no—
418C2×C4⋊C4—1464no—
419C2×C4⋊C4—1464no—
420C2×C4⋊C4—1464no—
421C2×C4⋊C4—1464no—
422C2×C4⋊C4—1464no—
423C2×C4⋊C4—1464no—
424C2×C4⋊C4—1464no—
425C2×C22⋊C4—734no—
426C2×C22⋊C4—734no—
427C2×C22⋊C4—1464no—
428C2×C22⋊C4—1464no—
429C2×C22⋊C4—1464no—
430C2×C22⋊C4—1464no—
431C2×C22⋊C4—1464no—
432C2×C22⋊C4—1464no—
433C2×C22⋊C4—1464no—
434C2×C22⋊C4—1464no—
435C2×C42—22no—
436C2×C42—22no—
437C2×C42—22no—
438C2×C42—22no—
439C2×C42—22no—
440C2×C42—22no—
441C2×C42—22no—
442C2×C42—734no—
443C2×C42—734no—
444C2×C42—1462no—
445C2×C42—1462no—
446C2×C42—1462no—
447C2×C42—1462no—
448C2×C42—1462no—
449C2×C42—1462no—
450C2×C42—1462no—
451C2×C42C4×D7314yes—
452C2×C42D29214yes—
453#95—24no—
454#95—24no—
455#95—734no—
456#95—734no—
457#95—1464no—
458#95—1464no—
459#95—1464no—
460#95—1464no—
461#95—1464no—
462C24—732no—
463C24—732no—
464C24—732no—
465C24—1461no—
466C24—1461no—
467C24—1462no—
468C24—1462no—
469C24—1461no—
470C24—1462no—
471C24—1462no—
472C24—1461no—
473C24C23×D7311yescharacteristic
474C22×C4—21no—
475C22×C4—22no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—21no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—732no—
494C22×C4—732no—
495C22×C4—732no—
496C22×C4—732no—
497C22×C4—734no—
498C22×C4—7316no—
499C22×C4—732no—
500C22×C4—734no—
501C22×C4—734no—
502C22×C4—1462no—
503C22×C4—1462no—
504C22×C4—1462no—
505C22×C4—1461no—
506C22×C4—1462no—
507C22×C4—1462no—
508C22×C4—1462no—
509C22×C4—1462no—
510C22×C4—1462no—
511C22×C4—1462no—
512C22×C4—1462no—
513C22×C4—1461no—
514C22×C4—1462no—
515C22×C4—1462no—
516C22×C4—1462no—
517C22×C4—1462no—
518C22×C4—1461no—
519C22×C4—1461no—
520C22×C4—1461no—
521C22×C4—1462no—
522C22×C4—1461no—
523C22×C4—1461no—
524C22×C4—1461no—
525C22×C4—1468no—
526C22×C4—1468no—
527C22×C4—1468no—
528C22×C4—1468no—
529C22×C4—1468no—
530C22×C4—1468no—
531C22×C4C2×C4×D7312yes—
532C22×C4C2×C4×D7312yes—
533C22×C4C2×C4×D7312yes—
534C22×C4D4×D7312yes—
535C22×C4D4×D7312yes—
536C22×C4C2×D29214yes—
537C22×C4C2×D29212yes—
538C22×C4Q8×D7312yes—
539C22×C4#1192402712yes—
540C22×C4#1192402814yes—
541C22×C4#1192402814yes—
542C22×C4#1192402812yes—
543C4⋊C4—14616no—
544C4⋊C4—14616no—
545C4⋊C4—14616no—
546C22⋊C4—1468no—
547C22⋊C4—14616no—
548C22⋊C4—14616no—
549C22⋊C4—1468no—
550C42—28no—
551C42—28no—
552C42—44no—
553C42—2924no—
554C42—1468no—
555C42—1468no—
556C23—2922no—
557C23—2922no—
558C23—2922no—
559C23—2922no—
560C23—2922no—
561C23—2922no—
562C23—2922no—
563C23—2922no—
564C23—734no—
565C23—1464no—
566C23—1464no—
567C23—1464no—
568C23—1462no—
569C23—1462no—
570C23—1462no—
571C23—1462no—
572C23—1462no—
573C23—1462no—
574C23—1462no—
575C23—1462no—
576C23—1462no—
577C23—1462no—
578C23—1464no—
579C23C22×C4×D7311yescharacteristic
580C23C2×D4×D7311yescharacteristic
581C23C2×D4×D7311yescharacteristic
582C23C22×D29211yescharacteristic
583C23C2×Q8×D7311yescharacteristic
584C23#41×D7312yes—
585C23#41×D7312yes—
586C23C2×#1192402711yescharacteristic
587C23C2×#1192402811yescharacteristic
588C23C2×#1192402812yes—
589C23C2×#1192402812yes—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—24no—
593C2×C4—24no—
594C2×C4—24no—
595C2×C4—24no—
596C2×C4—22no—
597C2×C4—22no—
598C2×C4—22no—
599C2×C4—24no—
600C2×C4—24no—
601C2×C4—24no—
602C2×C4—24no—
603C2×C4—42no—
604C2×C4—42no—
605C2×C4—42no—
606C2×C4—42no—
607C2×C4—42no—
608C2×C4—42no—
609C2×C4—42no—
610C2×C4—42no—
611C2×C4—42no—
612C2×C4—42no—
613C2×C4—2922no—
614C2×C4—2922no—
615C2×C4—2922no—
616C2×C4—2922no—
617C2×C4—2922no—
618C2×C4—2922no—
619C2×C4—2922no—
620C2×C4—2922no—
621C2×C4—2922no—
622C2×C4—2922no—
623C2×C4—734no—
624C2×C4—734no—
625C2×C4—1464no—
626C2×C4—1462no—
627C2×C4—1462no—
628C2×C4—1462no—
629C2×C4—1464no—
630C2×C4—1464no—
631C2×C4—1464no—
632C2×C4—1464no—
633C2×C4—1464no—
634C2×C4—1462no—
635C2×C4—1462no—
636C2×C4—1462no—
637C2×C4—1462no—
638C2×C4—1462no—
639C2×C4—1462no—
640C2×C4—1462no—
641C2×C4—1462no—
642C2×C4—1464no—
643C2×C4—1464no—
644C2×C4—14632no—
645C2×C4C4⋊C4×D7314yes—
646C2×C4#1455654814yescomplemented
647C2×C4#1455655114yes—
648C2×C4C4×D29214yes—
649C2×C4#1455656114yes—
650C2×C4#1455656914yes—
651C2×C4#1455657114yes—
652C2×C4#1455657314yes—
653C22—2922no—
654C22—2922no—
655C22—2924no—
656C22—2922no—
657C22—2922no—
658C22—2924no—
659C22—2924no—
660C22—2924no—
661C22—1464no—
662C22—1464no—
663C22—1464no—
664C22C2×C4⋊C4×D7311yescharacteristic
665C22#117×D7311yescharacteristic
666C22C2×#1455654811yescharacteristic
667C22C2×#1455655111yescharacteristic
668C22C2×C4×D29211yescharacteristic
669C22#1798905511yescharacteristic
670C22C4×#1192402811yescharacteristic
671C22C2×#1455656111yescharacteristic
672C22C2×#1455656911yescharacteristic
673C22C2×#1455657111yescharacteristic
674C22C2×#1455657311yescharacteristic
675C22#1798909612yes—
676C22#1798909612yes—
677C22#1798909912yes—
678C22#1798911512yes—
679C22#1798911712yes—
680C22#1798911712yes—
681C22#1798912112yes—
682C22#1798913412yes—
683C22#1798913412yes—
684C22#1798913712yes—
685C22#1798914112yes—
686C22#1798914112yes—
687C4—24no—
688C4—44no—
689C4—42no—
690C4—44no—
691C4—2924no—
692C4—2924no—
693C4—2922no—
694C4—1464no—
695C4—1464no—
696C4#1798846118yes—
697C2—2924no—
698C2#2261233511yescharacteristic
699C2C2×#1798846111yescharacteristic
700C2#2261237011yescharacteristic
701C2#2261237511yescharacteristic
702C2#2261239411yescharacteristic
703C2#2261239511yescharacteristic
704C2#2261241111yescharacteristic
705C2#2261314712yes—
706C2#2261319212yes—
707C2#2261320312yes—
708C2#2261320712yes—
subgroupG/H
centerC23×C4C22×D73
commutatorC23×C73C23×C4
FrattiniC24C23×D73
FittingC4×#95×C73C2
socle, cosocleC24×C73C24
prime radicalC24×D73C23
hypercenterC4×#95D73
hypocenterC73#13844
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23×C4 ◁ C4×#95

Complements

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

NH ≅ G/Ntype
2. C2×C4×#11924007C2semidirect
3. C2×C4×C4⋊Dic73C2semidirect
6. #22608195C2semidirect
7. #22608186C2semidirect
10. C4×#14556498C2semidirect
11. C4×#95×C73C2semidirect
29. C4×#11924005C4semidirect
155. C2×C4×D73C4⋊C4semidirect
259. C2×C4×C73#117semidirect
296. C2×Dic73#117semidirect
365. C4×#95D73semidirect
366. C73#13844semidirect
646. C2×C4#14556548semidirect

Maximal subgroups

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

subgroupindex
C22×#145565482
C2×C4×#119240072
C2×C4×C4⋊Dic732
C2×C4×#119240052
#226081952
#226081862
#226081772
#226081752
C4×#145564982
C4×#95×C732
#1384473