Subgroups — #17984176

Order 4384.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14555520	C₂	1	3	yes	maximal, complemented
2	#14555518	C₂	1	3	yes	maximal, complemented
3	#14555511	C₂	1	1	yes	maximal, characteristic
4	#11764047	C₂²	1	1	yes	characteristic
5	#11764047	C₂²	1	3	yes	—
6	D₅₄₈	C₄	1	3	yes	—
7	C₄×D₁₃₇	C₂²	1	3	yes	—
8	Q₈×C₁₃₇	C₄	1	1	yes	characteristic
9	C₂×D₁₃₇	C₂×C₄	1	3	yes	—
10	C₄×C₁₃₇	C₂×C₄	1	3	yes	—
11	Dic₁₃₇	C₂³	1	1	yes	characteristic
12	C₂×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
13	D₁₃₇	—	2	3	no	—
14	C₁₃₇	#131	1	1	yes	characteristic, complemented, Sylow
15	#131	—	137	1	no	maximal, Sylow
16	#41	—	137	1	no	—
17	M₁₆	—	137	3	no	—
18	C₂×C₈	—	137	3	no	—
19	Q₈	#10587739	1	1	yes	characteristic
20	D₄	—	137	3	no	—
21	C₂×C₄	—	137	3	no	—
22	C₈	—	137	1	no	—
23	C₈	—	137	3	no	—
24	C₂²	—	137	3	no	—
25	C₄	—	137	1	no	—
26	C₄	C₂×#10587739	1	3	yes	—
27	C₂	—	274	3	no	—
28	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.