Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
352 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 352 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 |
|---|---|---|
| 2. #10590283 | C2 | semidirect |
| 4. C3⋊C8×Dic6 | C2 | semidirect |
| 5. #10589347 | C2 | semidirect |
| 6. C3×#4480 | C2 | semidirect |
| 39. #4480 | D3 | semidirect |
| 284. C32 | #1678 | semidirect |
| 329. C3 | #68548 | semidirect |
| 330. C3 | #71022 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4848 | 2 |
| #10590283 | 2 |
| #10590273 | 2 |
| C3⋊C8×Dic6 | 2 |
| #10589347 | 2 |
| C3×#4480 | 2 |
| #10589090 | 2 |
| #71022 | 3 |
| #68548 | 3 |