Subgroups — #36342228

Order 21568.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#24925033	C₂	1	2	yes	maximal
2	C₄×#14582106	C₂	1	1	yes	maximal, characteristic
3	#19129188	—	2	2	no	—
4	C₂×#14582106	C₄	1	1	yes	characteristic
5	C₂×#14582106	C₂²	1	1	yes	characteristic
6	C₄²×C₃₃₇	C₄	1	1	yes	characteristic
7	#14582106	C₈	1	2	yes	—
8	#14582106	D₄	1	1	yes	characteristic
9	#14582106	Q₈	1	1	yes	characteristic
10	C₂×C₄×C₃₃₇	—	2	1	no	—
11	C₂×C₄×C₃₃₇	C₂×C₄	1	1	yes	characteristic
12	C₂²×C₃₃₇	M₁₆	1	1	yes	characteristic
13	C₄×C₃₃₇	—	2	2	no	—
14	C₄×C₃₃₇	C₄⋊C₄	1	1	yes	characteristic
15	C₄×C₃₃₇	C₂×C₈	1	1	yes	characteristic
16	C₂×C₃₃₇	—	2	1	no	—
17	C₂×C₃₃₇	C₄⋊C₈	1	1	yes	characteristic
18	C₃₃₇	#364	1	1	yes	characteristic, complemented, Sylow
19	#364	—	337	1	no	maximal, Sylow
20	M₃₂	—	337	2	no	—
21	C₄×C₈	—	337	1	no	—
22	C₂×C₈	—	337	1	no	—
23	C₂×C₈	—	337	1	no	—
24	C₄²	#13062438	1	1	yes	characteristic
25	C₁₆	—	674	2	no	—
26	C₂×C₄	—	2	1	no	—
27	C₂×C₄	C₂×#13062438	1	1	yes	characteristic
28	C₈	—	337	1	no	—
29	C₈	—	337	1	no	—
30	C₈	—	337	2	no	—
31	C₂²	#19129194	1	1	yes	characteristic
32	C₄	—	2	2	no	—
33	C₄	C₄⋊#13062438	1	1	yes	characteristic
34	C₄	#19129193	1	1	yes	characteristic
35	C₂	—	2	1	no	—
36	C₂	#24925026	1	1	yes	characteristic

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

N	H ≅ G/N	type
18. C₃₃₇	#364	semidirect

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