Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
339 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 339 conjugacy classes of subgroups — too many to draw. Only its 88 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 |
|---|---|---|
| 272. C32 | #1684 | semidirect |
| 310. C3 | #68591 | semidirect |
| 311. C3 | #71241 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C8×#634 | 2 |
| C3×#4681 | 2 |
| #10590307 | 2 |
| #10590284 | 2 |
| C3×#4458 | 2 |
| #10589095 | 2 |
| #10589092 | 2 |
| #71241 | 3 |
| #68591 | 3 |