Subgroups — C₂²×#622 #64291

Order 288.

130 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃⋊Dic₃	C₂	1	1	yes	maximal, characteristic
2	C₂×#622	C₂	1	6	yes	maximal, direct product factor
3	C₂³×C₃²	C₄	1	1	yes	characteristic
4	C₂×C₃⋊Dic₃	C₄	1	3	yes	—
5	C₂×C₃⋊Dic₃	C₂²	1	3	yes	—
6	#622	C₂²	1	4	yes	direct product factor
7	C₂²×Dic₃	—	6	2	no	—
8	C₂²×C₃²	C₈	1	4	yes	complemented
9	C₂²×C₃²	C₂×C₄	1	3	yes	—
10	C₃⋊Dic₃	C₂×C₄	1	3	yes	—
11	C₃⋊Dic₃	C₂³	1	1	yes	characteristic
12	C₂²×C₈	—	9	1	no	maximal, Sylow
13	C₂³×C₃	—	2	2	no	—
14	C₂×Dic₃	—	6	6	no	—
15	C₂×Dic₃	—	6	6	no	—
16	C₂×C₃²	C₂×C₈	1	6	yes	complemented
17	C₂×C₃²	C₂²×C₄	1	1	yes	characteristic
18	C₂²×C₄	—	9	1	no	—
19	C₂×C₈	—	9	6	no	—
20	C₂²×C₃	—	2	8	no	—
21	C₂²×C₃	—	2	6	no	—
22	Dic₃	—	6	6	no	—
23	Dic₃	—	6	2	no	—
24	C₃²	C₂²×C₈	1	1	yes	characteristic, complemented, Sylow
25	C₂³	#157	1	1	yes	characteristic
26	C₂×C₄	—	9	3	no	—
27	C₂×C₄	—	9	3	no	—
28	C₈	—	9	4	no	—
29	C₂×C₃	—	2	2	no	—
30	C₂×C₃	—	2	12	no	—
31	C₂²	#622	1	4	yes	direct product factor
32	C₂²	C₂×#157	1	3	yes	—
33	C₄	—	9	1	no	—
34	C₄	—	9	3	no	—
35	C₃	—	2	2	no	—
36	C₂	C₂×#622	1	6	yes	direct product factor
37	C₂	C₂²×#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.