Subgroups — #37560313

Order 23872.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26045867	C₂	1	1	yes	maximal, characteristic
2	#26045846	C₂	1	1	yes	maximal, characteristic
3	#26045731	C₂	1	1	yes	maximal, characteristic
4	D₃₇₃⋊C₈	C₄	1	1	yes	characteristic
5	C₄×#13093637	C₄	1	1	yes	characteristic
6	#20238613	C₄	1	2	yes	complemented
7	C₈×D₃₇₃	C₂²	1	1	yes	characteristic
8	#20238585	C₄	1	1	yes	characteristic, complemented
9	C₁₆×C₃₇₃	C₄	1	1	yes	characteristic, complemented
10	C₂×#13093637	—	2	1	no	—
11	#15688419	—	2	1	no	—
12	C₄×D₃₇₃	C₂×C₄	1	1	yes	characteristic
13	#15688412	C₂×C₄	1	1	yes	characteristic
14	C₈×C₃₇₃	C₂×C₄	1	1	yes	characteristic
15	C₂×D₃₇₃	M₁₆	1	1	yes	characteristic
16	#13093637	—	4	1	no	—
17	C₄×C₃₇₃	C₄²	1	1	yes	characteristic
18	Dic₃₇₃	M₁₆	1	1	yes	characteristic
19	C₂×C₃₇₃	#97	1	1	yes	characteristic
20	D₃₇₃	—	2	1	no	—
21	C₃₇₃	#347	1	1	yes	characteristic, complemented, Sylow
22	#347	—	373	1	no	maximal, Sylow
23	M₃₂	—	373	1	no	—
24	M₃₂	—	373	1	no	—
25	#97	—	373	1	no	—
26	C₂×C₈	—	373	1	no	—
27	C₂×C₈	—	373	1	no	—
28	C₄²	—	373	1	no	—
29	C₁₆	—	373	2	no	—
30	C₁₆	—	373	1	no	—
31	C₁₆	#13093637	1	1	yes	characteristic, complemented
32	C₂×C₄	—	373	1	no	—
33	C₂×C₄	—	746	1	no	—
34	C₈	—	373	1	no	—
35	C₈	—	746	1	no	—
36	C₈	C₂×#13093637	1	1	yes	characteristic
37	C₂²	—	373	1	no	—
38	C₄	—	373	1	no	—
39	C₄	—	1492	1	no	—
40	C₄	C₄×#13093637	1	1	yes	characteristic
41	C₂	—	746	1	no	—
42	C₂	#26045846	1	1	yes	characteristic

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

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