Subgroups — #17984152

Order 4384.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14555520	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×#10587739	C₂	1	1	yes	maximal, characteristic, complemented
3	#14555509	C₂	1	1	yes	maximal, characteristic
4	C₂×#10587739	—	2	1	no	—
5	#11764047	—	2	1	no	—
6	Dic₂₇₄	C₄	1	1	yes	characteristic, complemented
7	C₂²⋊D₁₃₇	—	2	1	no	—
8	C₂×Dic₁₃₇	—	2	1	no	—
9	C₄×D₁₃₇	C₂²	1	1	yes	characteristic
10	D₄×C₁₃₇	C₄	1	1	yes	characteristic, complemented
11	C₂²×C₁₃₇	—	2	1	no	—
12	C₂×D₁₃₇	D₄	1	1	yes	characteristic
13	#10587739	—	2	2	no	—
14	C₄×C₁₃₇	C₂×C₄	1	1	yes	characteristic
15	Dic₁₃₇	—	2	1	no	—
16	Dic₁₃₇	D₄	1	1	yes	characteristic
17	C₂×C₁₃₇	—	4	1	no	—
18	C₂×C₁₃₇	C₂²⋊C₄	1	1	yes	characteristic
19	D₁₃₇	—	2	1	no	—
20	C₁₃₇	#104	1	1	yes	characteristic, complemented, Sylow
21	#104	—	137	1	no	maximal, Sylow
22	#41	—	137	1	no	—
23	M₁₆	—	137	1	no	—
24	C₄²	—	137	1	no	—
25	Q₈	—	137	1	no	—
26	D₄	—	274	1	no	—
27	D₄	#10587739	1	1	yes	characteristic, complemented
28	C₂×C₄	—	274	1	no	—
29	C₂×C₄	—	274	1	no	—
30	C₂×C₄	—	137	1	no	—
31	C₈	—	274	1	no	—
32	C₂²	—	2	1	no	—
33	C₂²	—	137	1	no	—
34	C₄	—	274	2	no	—
35	C₄	—	274	1	no	—
36	C₄	—	137	1	no	—
37	C₄	C₂×#10587739	1	1	yes	characteristic
38	C₂	—	4	1	no	—
39	C₂	—	274	1	no	—
40	C₂	C₂²⋊#10587739	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.