Subgroups — C₂²×#11764049 #17984186

Order 4384.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11764049	C₂	1	6	yes	maximal, direct product factor
2	C₂²×#10587739	C₂	1	1	yes	maximal, characteristic
3	#11764049	C₂²	1	4	yes	direct product factor
4	C₂×#10587739	C₄	1	3	yes	—
5	C₂×#10587739	C₂²	1	3	yes	—
6	C₂²×D₁₃₇	C₄	1	1	yes	characteristic
7	C₂²×C₁₃₇	C₈	1	1	yes	characteristic, complemented
8	C₂×D₁₃₇	C₈	1	3	yes	complemented
9	C₂×D₁₃₇	C₂×C₄	1	3	yes	—
10	#10587739	C₂×C₄	1	3	yes	—
11	#10587739	C₂³	1	1	yes	characteristic
12	C₂×C₁₃₇	C₂×C₈	1	3	yes	complemented
13	D₁₃₇	C₂×C₈	1	3	yes	complemented
14	D₁₃₇	C₂²×C₄	1	1	yes	characteristic
15	C₁₃₇	C₂²×C₈	1	1	yes	characteristic, complemented, Sylow
16	C₂²×C₈	—	137	1	no	maximal, Sylow
17	C₂²×C₄	—	137	1	no	—
18	C₂×C₈	—	137	6	no	—
19	C₂³	—	137	1	no	—
20	C₂×C₄	—	137	3	no	—
21	C₂×C₄	—	137	3	no	—
22	C₈	—	137	4	no	—
23	C₂²	—	137	3	no	—
24	C₂²	—	137	3	no	—
25	C₂²	#11764049	1	1	yes	characteristic, direct product factor
26	C₄	—	137	1	no	—
27	C₄	—	137	3	no	—
28	C₂	—	137	1	no	—
29	C₂	—	137	3	no	—
30	C₂	C₂×#11764049	1	3	yes	direct product factor

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.