Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
286 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 77 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 |
|---|---|---|
| 15. #63746 | C4 | semidirect |
| 56. #622 | C4⋊C4 | semidirect |
| 140. C32 | #1942 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C8×#157 | 2 |
| #10593554 | 2 |
| C2×#63746 | 2 |
| #10590182 | 2 |
| #1942 | 9 |