Subgroups — C₂²×#13182032 #20296079

Order 6976.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13182032	C₂	1	6	yes	maximal, direct product factor
2	C₂²×#11724784	C₂	1	1	yes	maximal, characteristic
3	#13182032	C₂²	1	4	yes	direct product factor
4	C₂×#11724784	C₄	1	3	yes	—
5	C₂×#11724784	C₂²	1	3	yes	—
6	C₂²×C₄×C₁₀₉	C₄	1	1	yes	characteristic
7	C₂³×C₁₀₉	C₈	1	1	yes	characteristic
8	C₂×C₄×C₁₀₉	C₈	1	3	yes	—
9	C₂×C₄×C₁₀₉	C₂×C₄	1	3	yes	—
10	#11724784	C₂×C₄	1	3	yes	—
11	#11724784	C₂³	1	1	yes	characteristic
12	C₂²×C₁₀₉	C₁₆	1	4	yes	complemented
13	C₂²×C₁₀₉	C₂×C₈	1	3	yes	—
14	C₄×C₁₀₉	C₂×C₈	1	3	yes	—
15	C₄×C₁₀₉	C₂²×C₄	1	1	yes	characteristic
16	C₂×C₁₀₉	C₂×C₁₆	1	6	yes	complemented
17	C₂×C₁₀₉	C₂²×C₈	1	1	yes	characteristic
18	C₁₀₉	C₂²×C₁₆	1	1	yes	characteristic, complemented, Sylow
19	C₂²×C₁₆	—	109	1	no	maximal, Sylow
20	C₂²×C₈	—	109	1	no	—
21	C₂×C₁₆	—	109	6	no	—
22	C₂²×C₄	#89137	1	1	yes	characteristic
23	C₂×C₈	—	109	3	no	—
24	C₂×C₈	—	109	3	no	—
25	C₁₆	—	109	4	no	—
26	C₂³	#11724786	1	1	yes	characteristic
27	C₂×C₄	#11724786	1	3	yes	—
28	C₂×C₄	C₂×#89137	1	3	yes	—
29	C₈	—	109	1	no	—
30	C₈	—	109	3	no	—
31	C₂²	#13182032	1	4	yes	direct product factor
32	C₂²	C₂×#11724786	1	3	yes	—
33	C₄	C₂×#11724786	1	3	yes	—
34	C₄	C₂²×#89137	1	1	yes	characteristic
35	C₂	C₂×#13182032	1	6	yes	direct product factor
36	C₂	C₂²×#11724786	1	1	yes	characteristic

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