Subgroups — C₂²×#157 #3848

Order 144.

86 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	6	yes	maximal, direct product factor
3	C₂²×C₃²	C₄	1	1	yes	characteristic, complemented
4	C₂×C₃⋊D₃	C₄	1	3	yes	complemented
5	C₂×C₃⋊D₃	C₂²	1	3	yes	—
6	#157	C₂²	1	4	yes	direct product factor
7	C₂²×D₃	—	6	2	no	—
8	C₂×C₃²	C₂×C₄	1	3	yes	complemented
9	C₃⋊D₃	C₂×C₄	1	3	yes	complemented
10	C₃⋊D₃	C₂³	1	1	yes	characteristic
11	C₂²×C₄	—	9	1	no	maximal, Sylow
12	C₂²×C₃	—	2	2	no	—
13	C₂×D₃	—	6	6	no	—
14	C₂×D₃	—	6	6	no	—
15	C₃²	C₂²×C₄	1	1	yes	characteristic, complemented, Sylow
16	C₂³	—	9	1	no	—
17	C₂×C₄	—	9	6	no	—
18	C₂×C₃	—	2	6	no	—
19	D₃	—	6	6	no	—
20	D₃	—	6	2	no	—
21	C₂²	—	9	3	no	—
22	C₂²	—	9	3	no	—
23	C₂²	#157	1	1	yes	characteristic, direct product factor
24	C₄	—	9	4	no	—
25	C₃	—	2	2	no	—
26	C₂	—	9	1	no	—
27	C₂	—	9	3	no	—
28	C₂	C₂×#157	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.