Finite Group Databasebeta

← #33009217

Subgroups — #33009217

Order 18688.

1470 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988485C211yesmaximal, characteristic
2C2×#17988485C211yesmaximal, characteristic
3C2×#17988485C211yesmaximal, characteristic
4C2×#17988453C211yesmaximal, characteristic
5C2×C4×C4⋊Dic73C211yesmaximal, characteristic
6#22608189C212yesmaximal
7#22608182C212yesmaximal
8#22608162C212yesmaximal
9#22608161C211yesmaximal, characteristic
10#22608159C212yesmaximal
11C4×#95×C73C211yesmaximal, characteristic
12C22×C4⋊Dic73C2211yescharacteristic
13C22×C4⋊Dic73C2211yescharacteristic
14C22×C4⋊Dic73C2211yescharacteristic
15C22×C4⋊Dic73C2211yescharacteristic
16C22×#11924007C2212yes—
17C22×#11924007C2212yes—
18C22×#11924007C2212yes—
19C22×C4×Dic73C2212yes—
20#17988485—24no—
21#17988485—24no—
22#17988485C418yescomplemented
23#17988453—24no—
24C4×C4⋊Dic73—24no—
25C2×#14556498C2212yes—
26C2×#14556498C2212yes—
27C2×#14556498C2212yes—
28C2×#14556498C2212yes—
29C2×#14556498C2212yes—
30C2×#14556498C2212yes—
31C2×#14556498C2212yes—
32C2×#14556498C2212yes—
33C22×C42×C73C2211yescharacteristic
34C22×C42×C73C2211yescharacteristic
35C22×C42×C73C2211yescharacteristic
36C2×#95×C73C2211yescharacteristic
37C2×#95×C73C2211yescharacteristic
38C2×#95×C73C2211yescharacteristic
39C2×#95×C73C2211yescharacteristic
40C23×Dic73C2312yes—
41C23×Dic73C2312yes—
42C23×Dic73C2312yes—
43C23×Dic73C2312yes—
44C2×C4⋊Dic73—22no—
45C2×C4⋊Dic73—22no—
46C2×C4⋊Dic73—22no—
47C2×C4⋊Dic73—22no—
48C2×C4⋊Dic73—22no—
49C2×C4⋊Dic73—22no—
50C2×C4⋊Dic73—22no—
51C2×C4⋊Dic73C2×C414yes—
52C2×C4⋊Dic73C2×C414yes—
53C2×C4⋊Dic73D414yes—
54C2×C4⋊Dic73D414yes—
55C2×C4⋊Dic73Q814yes—
56C2×#11924007—24no—
57C2×#11924007—24no—
58C2×#11924007—24no—
59C2×#11924007—24no—
60C2×#11924007—42no—
61C2×#11924007—42no—
62C2×#11924007—42no—
63C2×#11924007—42no—
64C2×#11924007C2×C418yes—
65C2×C4×Dic73—24no—
66C2×C4×Dic73—24no—
67C2×C4×Dic73—42no—
68#14556498—24no—
69#14556498—24no—
70#14556498—24no—
71#14556498—24no—
72#14556498—24no—
73#14556498—24no—
74#14556498—42no—
75#14556498C2×C418yes—
76C23×C4×C73C2311yescharacteristic
77C23×C4×C73C2311yescharacteristic
78C23×C4×C73C2311yescharacteristic
79C23×C4×C73C2311yescharacteristic
80C23×C4×C73C2311yescharacteristic
81C23×C4×C73C2311yescharacteristic
82C23×C4×C73C2311yescharacteristic
83C2×C42×C73—22no—
84C2×C42×C73—22no—
85C2×C42×C73—22no—
86C2×C42×C73—22no—
87C2×C42×C73—22no—
88C2×C42×C73—22no—
89C2×C42×C73—22no—
90C2×C42×C73C2×C414yes—
91C2×C42×C73Q814yes—
92#95×C73—22no—
93#95×C73—22no—
94#95×C73—22no—
95#95×C73—22no—
96C22×Dic73—22no—
97C22×Dic73—22no—
98C22×Dic73—22no—
99C22×Dic73—22no—
100C22×Dic73—22no—
101C22×Dic73—22no—
102C22×Dic73—22no—
103C22×Dic73—22no—
104C22×Dic73—22no—
105C22×Dic73—22no—
106C22×Dic73—22no—
107C22×Dic73—22no—
108C22×Dic73—22no—
109C22×Dic73—22no—
110C22×Dic73—22no—
111C22×Dic73—22no—
112C22×Dic73—22no—
113C22×Dic73—22no—
114C22×Dic73—22no—
115C22×Dic73—22no—
116C22×Dic73—22no—
117C22×Dic73—22no—
118C22×Dic73—22no—
119C22×Dic73C22×C414yes—
120C22×Dic73C22×C414yes—
121C22×Dic73C2×D414yes—
122C22×Dic73C2×D414yes—
123C22×Dic73C2×Q814yes—
124C4⋊Dic73—28no—
125C4⋊Dic73—28no—
126C4⋊Dic73—44no—
127C4⋊Dic73C4⋊C4116yescomplemented
128#11924007—48no—
129#11924007—48no—
130#11924007—48no—
131C4×Dic73—48no—
132C24×C73C2411yescharacteristic
133C22×C4×C73—21no—
134C22×C4×C73—21no—
135C22×C4×C73—21no—
136C22×C4×C73—21no—
137C22×C4×C73—21no—
138C22×C4×C73—21no—
139C22×C4×C73—21no—
140C22×C4×C73—21no—
141C22×C4×C73—21no—
142C22×C4×C73—21no—
143C22×C4×C73—21no—
144C22×C4×C73—21no—
145C22×C4×C73—21no—
146C22×C4×C73—21no—
147C22×C4×C73—21no—
148C22×C4×C73—21no—
149C22×C4×C73—21no—
150C22×C4×C73—21no—
151C22×C4×C73—21no—
152C22×C4×C73—21no—
153C22×C4×C73—21no—
154C22×C4×C73—21no—
155C22×C4×C73—21no—
156C22×C4×C73—21no—
157C22×C4×C73—21no—
158C22×C4×C73—21no—
159C22×C4×C73—21no—
160C22×C4×C73—21no—
161C22×C4×C73—21no—
162C22×C4×C73—21no—
163C22×C4×C73—21no—
164C22×C4×C73—21no—
165C22×C4×C73—21no—
166C22×C4×C73—21no—
167C22×C4×C73C22×C412yes—
168C22×C4×C73C22×C412yes—
169C22×C4×C73C22×C412yes—
170C22×C4×C73C2×D412yes—
171C22×C4×C73C2×D412yes—
172C22×C4×C73C2×Q812yes—
173C22×C4×C73C2×Q812yes—
174C22×C4×C73C2×Q812yes—
175C22×C4×C73C2×Q812yes—
176C22×C4×C73#4112yes—
177C22×C4×C73#4112yes—
178C22×C4×C73#4112yes—
179C22×C4×C73#4112yes—
180C22×C4×C73#4112yes—
181C22×C4×C73#4112yes—
182C42×C73—28no—
183C42×C73—28no—
184C42×C73—44no—
185C23×C73C23×C411yescharacteristic
186C23×C73C22×D411yescharacteristic
187C23×C73C22×D411yescharacteristic
188C23×C73C22×Q811yescharacteristic
189C23×C73C22×Q811yescharacteristic
190C23×C73C2×#4111yescharacteristic
191C23×C73C2×#4111yescharacteristic
192C23×C73C2×#4111yescharacteristic
193C23×C73C2×#4111yescharacteristic
194C23×C73C2×#4111yescharacteristic
195C23×C73C2×#4111yescharacteristic
196C23×C73H(5,𝔽2)11yescharacteristic
197C23×C73H(5,𝔽2)11yescharacteristic
198C23×C732−1+411yescharacteristic
199C23×C732−1+411yescharacteristic
200C2×C4×C73—22no—
201C2×C4×C73—22no—
202C2×C4×C73—22no—
203C2×C4×C73—22no—
204C2×C4×C73—22no—
205C2×C4×C73—22no—
206C2×C4×C73—22no—
207C2×C4×C73—22no—
208C2×C4×C73—22no—
209C2×C4×C73—22no—
210C2×C4×C73—22no—
211C2×C4×C73—22no—
212C2×C4×C73—22no—
213C2×C4×C73—22no—
214C2×C4×C73—22no—
215C2×C4×C73—22no—
216C2×C4×C73—22no—
217C2×C4×C73—22no—
218C2×C4×C73—22no—
219C2×C4×C73—22no—
220C2×C4×C73—22no—
221C2×C4×C73—41no—
222C2×C4×C73—41no—
223C2×C4×C73—41no—
224C2×C4×C73—41no—
225C2×C4×C73—41no—
226C2×C4×C73—41no—
227C2×C4×C73—41no—
228C2×C4×C73—41no—
229C2×C4×C73—41no—
230C2×C4×C73—41no—
231C2×C4×C73—41no—
232C2×C4×C73—41no—
233C2×C4×C73—41no—
234C2×C4×C73—41no—
235C2×C4×C73—41no—
236C2×C4×C73—41no—
237C2×C4×C73—41no—
238C2×C4×C73—41no—
239C2×C4×C73—41no—
240C2×C4×C73—41no—
241C2×C4×C73C2×C4⋊C414yes—
242C2×C4×C73C4×D414yes—
243C2×C4×C73C4×Q814yes—
244C2×C4×C73#12114yes—
245C2×C4×C73C22⋊Q814yes—
246C2×C4×C73#12514yes—
247C2×C4×C73#12514yes—
248C2×C4×C73C4⋊Q814yes—
249C2×Dic73—24no—
250C2×Dic73—24no—
251C2×Dic73—24no—
252C2×Dic73—24no—
253C2×Dic73—24no—
254C2×Dic73—24no—
255C2×Dic73—24no—
256C2×Dic73—24no—
257C2×Dic73—24no—
258C2×Dic73—24no—
259C2×Dic73—24no—
260C2×Dic73—24no—
261C2×Dic73—42no—
262C2×Dic73—42no—
263C2×Dic73—42no—
264C2×Dic73—42no—
265C2×Dic73—42no—
266C2×Dic73—42no—
267C2×Dic73—42no—
268C2×Dic73—42no—
269C2×Dic73—42no—
270C2×Dic73—42no—
271C2×Dic73—42no—
272C2×Dic73—42no—
273C2×Dic73—42no—
274C2×Dic73—42no—
275C2×Dic73—42no—
276C2×Dic73C2×C4⋊C418yes—
277C22×C73C22×C4⋊C411yescharacteristic
278C22×C73C2×C4×D411yescharacteristic
279C22×C73C2×C4×Q811yescharacteristic
280C22×C73C4×#4111yescharacteristic
281C22×C73C4×#4111yescharacteristic
282C22×C73#51811yescharacteristic
283C22×C73#51911yescharacteristic
284C22×C73C2×#12111yescharacteristic
285C22×C73C2×C22⋊Q811yescharacteristic
286C22×C73C2×#12511yescharacteristic
287C22×C73C2×#12511yescharacteristic
288C22×C73#52911yescharacteristic
289C22×C73#52911yescharacteristic
290C22×C73C2×C4⋊Q811yescharacteristic
291C22×C73#53311yescharacteristic
292C22×C73#54211yescharacteristic
293C22×C73#54211yescharacteristic
294C22×C73#54411yescharacteristic
295C22×C73#54411yescharacteristic
296C22×C73#54611yescharacteristic
297C22×C73#54611yescharacteristic
298C22×C73#54611yescharacteristic
299C22×C73#54711yescharacteristic
300C22×C73#54811yescharacteristic
301C22×C73#54811yescharacteristic
302C22×C73#54811yescharacteristic
303C22×C73#55011yescharacteristic
304C22×C73#55211yescharacteristic
305C22×C73#55311yescharacteristic
306C22×C73#55411yescharacteristic
307C22×C73#55411yescharacteristic
308C22×C73#55511yescharacteristic
309C22×C73#55611yescharacteristic
310C22×C73#55711yescharacteristic
311C22×C73#55711yescharacteristic
312C4×C73—24no—
313C4×C73—42no—
314C4×C73—42no—
315C4×C73—42no—
316C4×C73—42no—
317C4×C73—42no—
318C4×C73#38918yes—
319Dic73—28no—
320Dic73—44no—
321Dic73—44no—
322Dic73—82no—
323#14006—731nomaximal, Sylow
324C2×C73C2×#38911yescharacteristic
325C2×C73C4×#12511yescharacteristic
326C2×C73#233111yescharacteristic
327C2×C73#234911yescharacteristic
328C2×C73#235111yescharacteristic
329C2×C73#236211yescharacteristic
330C2×C73#236311yescharacteristic
331C2×C73#242611yescharacteristic
332C2×C73#242711yescharacteristic
333C2×C73#243911yescharacteristic
334C2×C73#244211yescharacteristic
335C2×C73#250811yescharacteristic
336C2×C73#250911yescharacteristic
337C2×C73#255011yescharacteristic
338C2×C73#255211yescharacteristic
339C2×#389—731no—
340C2×#389—731no—
341C2×#389—731no—
342C2×#382—731no—
343C2×C4×C4⋊C4—731no—
344#1442—732no—
345#1441—732no—
346#1436—732no—
347C4⋊#95—731no—
348C4⋊#95—732no—
349C4×#95D7311yescharacteristic
350C73#1400611yescharacteristic, complemented, Sylow
351C22×C4⋊C4—732no—
352C22×C4⋊C4—732no—
353C22×C4⋊C4—732no—
354C22×C4⋊C4—731no—
355C22×C4⋊C4—731no—
356C22×C4⋊C4—731no—
357C22×C4⋊C4—731no—
358C22×C42—732no—
359C22×C42C2×D7311yescharacteristic
360C22×C42C2×D7311yescharacteristic
361C22×C42C2×D7311yescharacteristic
362#389—738no—
363#389—1464no—
364#389—1464no—
365#382—1464no—
366C4×C4⋊C4—1464no—
367C2×#95—732no—
368C2×#95—732no—
369C2×#95—732no—
370C2×#95—732no—
371C2×#95—732no—
372C2×#95—732no—
373C2×#95—732no—
374C2×#95—732no—
375C2×#95C2×D7311yescharacteristic
376C2×#95C2×D7311yescharacteristic
377C2×#95C2×D7311yescharacteristic
378C2×#95C2×D7311yescharacteristic
379C23×C4—732no—
380C23×C4—732no—
381C23×C4—732no—
382C23×C4—732no—
383C23×C4C22×D7311yescharacteristic
384C23×C4C22×D7311yescharacteristic
385C23×C4C22×D7311yescharacteristic
386C23×C4C22×D7311yescharacteristic
387C23×C4C22×D7311yescharacteristic
388C23×C4C22×D7311yescharacteristic
389C23×C4C22×D7311yescharacteristic
390C2×C4⋊C4—2922no—
391C2×C4⋊C4—2922no—
392C2×C4⋊C4—2922no—
393C2×C4⋊C4—2922no—
394C2×C4⋊C4—738no—
395C2×C4⋊C4—734no—
396C2×C4⋊C4—734no—
397C2×C4⋊C4—734no—
398C2×C4⋊C4—734no—
399C2×C4⋊C4—734no—
400C2×C4⋊C4—1464no—
401C2×C4⋊C4—1464no—
402C2×C4⋊C4—1462no—
403C2×C4⋊C4—1462no—
404C2×C4⋊C4—1464no—
405C2×C4⋊C4—1464no—
406C2×C4⋊C4—1462no—
407C2×C4⋊C4—1462no—
408C2×C4⋊C4—1462no—
409C2×C4⋊C4—1462no—
410C2×C4⋊C4—1462no—
411C2×C42—22no—
412C2×C42—22no—
413C2×C42—22no—
414C2×C42—22no—
415C2×C42—22no—
416C2×C42—22no—
417C2×C42—22no—
418C2×C42—2922no—
419C2×C42—1464no—
420C2×C42—1464no—
421C2×C42Dic14614yes—
422C2×C42C4×D7314yes—
423#95—22no—
424#95—22no—
425#95—22no—
426#95—22no—
427#95—2922no—
428#95—738no—
429#95—1464no—
430#95—1464no—
431#95—1464no—
432#95—1464no—
433#95—1464no—
434#95—1464no—
435C24C23×D7311yescharacteristic
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—734no—
471C22×C4—734no—
472C22×C4—734no—
473C22×C4—734no—
474C22×C4—734no—
475C22×C4—1462no—
476C22×C4—1462no—
477C22×C4—1462no—
478C22×C4—1462no—
479C22×C4—1462no—
480C22×C4—1462no—
481C22×C4—1462no—
482C22×C4—1462no—
483C22×C4—1462no—
484C22×C4—1462no—
485C22×C4—1462no—
486C22×C4—1462no—
487C22×C4—1462no—
488C22×C4—1462no—
489C22×C4—1462no—
490C22×C4—1462no—
491C22×C4—1462no—
492C22×C4—1462no—
493C22×C4—1462no—
494C22×C4—1462no—
495C22×C4—1462no—
496C22×C4—1462no—
497C22×C4—1462no—
498C22×C4C2×C4×D7312yes—
499C22×C4C2×C4×D7312yes—
500C22×C4C2×C4×D7312yes—
501C22×C4D4×D7312yes—
502C22×C4D4×D7312yes—
503C22×C4Q8×D7312yes—
504C22×C4C2×Dic14612yes—
505C22×C4C2×Dic14612yes—
506C22×C4C2×Dic14612yes—
507C22×C4#1192402712yes—
508C22×C4#1192402812yes—
509C22×C4#1192402812yes—
510C22×C4#1192402812yes—
511C22×C4#1192402812yes—
512C22×C4#1192402812yes—
513C4⋊C4—2928no—
514C4⋊C4—2928no—
515C4⋊C4—2928no—
516C4⋊C4—2924no—
517C4⋊C4—7316no—
518C4⋊C4—1468no—
519C4⋊C4—1468no—
520C42—28no—
521C42—28no—
522C42—44no—
523C42—2928no—
524C23C22×C4×D7311yescharacteristic
525C23C2×D4×D7311yescharacteristic
526C23C2×D4×D7311yescharacteristic
527C23C2×Q8×D7311yescharacteristic
528C23C22×Dic14611yescharacteristic
529C23C2×#1192402711yescharacteristic
530C23C2×#1192402811yescharacteristic
531C23C2×#1192402811yescharacteristic
532C23C2×#1192402811yescharacteristic
533C23C2×#1192402811yescharacteristic
534C23C2×#1192402811yescharacteristic
535C23#1455663711yescharacteristic
536C23#1455663711yescharacteristic
537C23#1455663811yescharacteristic
538C23#1455663811yescharacteristic
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—22no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—2922no—
581C2×C4—2922no—
582C2×C4—2922no—
583C2×C4—2922no—
584C2×C4—2922no—
585C2×C4—2922no—
586C2×C4—2922no—
587C2×C4—2922no—
588C2×C4—2922no—
589C2×C4—2922no—
590C2×C4—2922no—
591C2×C4—2922no—
592C2×C4—2922no—
593C2×C4—2922no—
594C2×C4—2922no—
595C2×C4—738no—
596C2×C4—1464no—
597C2×C4—1464no—
598C2×C4—1464no—
599C2×C4—1464no—
600C2×C4—1464no—
601C2×C4—1464no—
602C2×C4—1464no—
603C2×C4—1464no—
604C2×C4—1464no—
605C2×C4—1464no—
606C2×C4—1464no—
607C2×C4—1464no—
608C2×C4C4⋊C4×D7314yes—
609C2×C4#1455655114yes—
610C2×C4C4×Dic14614yes—
611C2×C4#1455656414yes—
612C2×C4#1455656814yes—
613C2×C4#1455658114yes—
614C2×C4#1455658314yes—
615C2×C4#1455659014yes—
616C22C2×C4⋊C4×D7311yescharacteristic
617C22C2×#1455655111yescharacteristic
618C22C2×C4×Dic14611yescharacteristic
619C22C4×#1192402811yescharacteristic
620C22C4×#1192402811yescharacteristic
621C22#1798906111yescharacteristic
622C22#1798906411yescharacteristic
623C22C2×#1455656411yescharacteristic
624C22C2×#1455656811yescharacteristic
625C22C2×#1455658111yescharacteristic
626C22C2×#1455658311yescharacteristic
627C22#1798912111yescharacteristic
628C22#1798912111yescharacteristic
629C22C2×#1455659011yescharacteristic
630C22#1798914411yescharacteristic
631C22#1798920811yescharacteristic
632C22#1798920811yescharacteristic
633C22#1798921511yescharacteristic
634C22#1798921511yescharacteristic
635C22#1798923311yescharacteristic
636C22#1798923311yescharacteristic
637C22#1798923311yescharacteristic
638C22#1798924211yescharacteristic
639C22#1798924611yescharacteristic
640C22#1798924611yescharacteristic
641C22#1798924611yescharacteristic
642C22#1798925811yescharacteristic
643C22#1798927711yescharacteristic
644C22#1798928311yescharacteristic
645C22#1798929711yescharacteristic
646C22#1798929711yescharacteristic
647C22#1798930211yescharacteristic
648C22#1798930711yescharacteristic
649C22#1798931511yescharacteristic
650C22#1798931511yescharacteristic
651C4—24no—
652C4—42no—
653C4—42no—
654C4—42no—
655C4—42no—
656C4—42no—
657C4—2924no—
658C4—2924no—
659C4—5842no—
660C4—1468no—
661C4#1798848418yes—
662C2C2×#1798848411yescharacteristic
663C2C4×#1455658311yescharacteristic
664C2#2261267911yescharacteristic
665C2#2261284211yescharacteristic
666C2#2261285111yescharacteristic
667C2#2261295611yescharacteristic
668C2#2261296711yescharacteristic
669C2#2261349711yescharacteristic
670C2#2261350811yescharacteristic
671C2#2261362211yescharacteristic
672C2#2261365511yescharacteristic
673C2#2261446911yescharacteristic
674C2#2261448011yescharacteristic
675C2#2261495211yescharacteristic
676C2#2261496611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D73
commutatorC23×C73C23×C4
FittingC4×#95×C73C2
socle, prime radical, cosocleC24×C73C24
hypercenterC4×#95D73
hypocenterC73#14006
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C24 ◁ C4×#95

Complements

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

NH ≅ G/Ntype
22. #17988485C4semidirect
127. C4⋊Dic73C4⋊C4semidirect
350. C73#14006semidirect

Maximal subgroups

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

subgroupindex
C2×#179884852
C2×#179884532
C2×C4×C4⋊Dic732
#226081892
#226081822
#226081622
#226081612
#226081592
C4×#95×C732
#1400673