Subgroups — C₂²×Dic₃₈₆ #20259939

Order 6176.

156 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₃₈₆	C₂	1	12	yes	maximal, direct product factor
2	C₂²×Dic₁₉₃	C₂	1	2	yes	maximal
3	C₂²×C₄×C₁₉₃	C₂	1	1	yes	maximal, characteristic
4	Dic₃₈₆	C₂²	1	16	yes	direct product factor
5	C₂×Dic₁₉₃	C₂²	1	12	yes	—
6	C₂³×C₁₉₃	C₂²	1	1	yes	characteristic
7	C₂×C₄×C₁₉₃	C₂²	1	6	yes	—
8	C₂²×C₁₉₃	Q₈	1	4	yes	complemented
9	C₂²×C₁₉₃	C₂³	1	3	yes	—
10	C₄×C₁₉₃	C₂³	1	4	yes	—
11	Dic₁₉₃	C₂³	1	8	yes	—
12	C₂×C₁₉₃	C₂×Q₈	1	6	yes	complemented
13	C₂×C₁₉₃	C₂⁴	1	1	yes	characteristic
14	C₁₉₃	C₂²×Q₈	1	1	yes	characteristic, complemented, Sylow
15	C₂²×Q₈	—	193	1	no	maximal, Sylow
16	C₂×Q₈	—	193	12	no	—
17	C₂²×C₄	—	193	2	no	—
18	C₂²×C₄	D₁₉₃	1	1	yes	characteristic
19	C₂³	C₂×D₁₉₃	1	1	yes	characteristic
20	Q₈	—	193	16	no	—
21	C₂×C₄	—	193	12	no	—
22	C₂×C₄	C₂×D₁₉₃	1	6	yes	—
23	C₂²	Dic₃₈₆	1	4	yes	direct product factor
24	C₂²	C₂²×D₁₉₃	1	3	yes	—
25	C₄	—	193	8	no	—
26	C₄	C₂²×D₁₉₃	1	4	yes	—
27	C₂	C₂×Dic₃₈₆	1	6	yes	direct product factor
28	C₂	C₂³×D₁₉₃	1	1	yes	characteristic

Splittings G = N ⋊ H with N normal; H ≅ G/N.