Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1656 conjugacy classes of subgroups; only the 377 normal subgroups are shown.
This group has 1656 conjugacy classes of subgroups — too many to draw. Only its 377 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 5. #10592882 | C2 | direct (N × H) |
| 79. C2×C3⋊Dic3 | Q16 | semidirect |
| 122. C3⋊Dic3 | C2×Q16 | semidirect |
| 157. C2×C32 | #494 | semidirect |
| 191. C32 | C2×#494 | semidirect |
| 211. C2×C3 | #5183 | semidirect |
| 223. C3 | C2×#5183 | semidirect |
| 224. C2 | #10592882 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C32×Q16 | 2 |
| C2×#64153 | 2 |
| C22×#3756 | 2 |
| C22×#3746 | 2 |
| #10592882 | 2 |
| C2×C8×C3⋊Dic3 | 2 |
| C2×#5183 | 3 |