Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
588 conjugacy classes of subgroups; only the 191 normal subgroups are shown.
This group has 588 conjugacy classes of subgroups — too many to draw. Only its 191 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 |
|---|---|---|
| 16. #63649 | C4 | semidirect |
| 211. C32 | #1952 | semidirect |
| 248. C3 | #68985 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#63649 | 2 |
| #10592821 | 2 |
| #10592820 | 2 |
| #10592663 | 2 |
| C2×#63634 | 2 |
| C32×#343 | 2 |
| #10589420 | 2 |
| #68985 | 3 |