Subgroups — C₂²⋊#157 #3793

Order 144.

66 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic
2	C₂×#157	C₂	1	2	yes	maximal, complemented
3	C₂²×C₃²	C₄	1	1	yes	characteristic, complemented
4	C₂×C₃⋊D₃	—	2	2	no	—
5	C₂×C₃⋊D₃	C₄	1	1	yes	characteristic, complemented
6	C₂×C₃⋊D₃	C₂²	1	1	yes	characteristic
7	#157	—	2	2	no	—
8	C₂²×D₃	—	6	2	no	—
9	C₂×C₃²	—	2	1	no	—
10	C₂×C₃²	C₂×C₄	1	1	yes	characteristic
11	C₃⋊D₃	—	2	1	no	—
12	C₃⋊D₃	D₄	1	2	yes	—
13	C₂²⋊C₄	—	9	1	no	maximal, Sylow
14	C₂²×C₃	—	2	2	no	—
15	C₂×D₃	—	6	2	no	—
16	C₂×D₃	—	6	2	no	—
17	C₂×D₃	—	6	8	no	—
18	C₃²	C₂²⋊C₄	1	1	yes	characteristic, complemented, Sylow
19	C₂³	—	9	1	no	—
20	C₂×C₄	—	9	2	no	—
21	C₂×C₃	—	2	4	no	—
22	C₂×C₃	—	2	2	no	—
23	D₃	—	6	4	no	—
24	D₃	—	6	4	no	—
25	C₂²	—	9	1	no	—
26	C₂²	—	9	1	no	—
27	C₂²	—	18	2	no	—
28	C₂²	#157	1	1	yes	characteristic, complemented
29	C₄	—	18	2	no	—
30	C₃	—	2	2	no	—
31	C₂	—	2	1	no	—
32	C₂	—	9	2	no	—
33	C₂	—	18	1	no	—
34	C₂	C₂×#157	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.