Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
359 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 359 conjugacy classes of subgroups — too many to draw. Only its 86 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. #10590384 | C2 | semidirect |
| 4. #10590250 | C2 | semidirect |
| 5. #10589345 | C2 | semidirect |
| 6. C3×#4482 | C2 | semidirect |
| 36. #4482 | D3 | semidirect |
| 289. C32 | #1682 | semidirect |
| 335. C3 | #68470 | semidirect |
| 336. C3 | #71023 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4848 | 2 |
| #10590384 | 2 |
| #10590277 | 2 |
| #10590250 | 2 |
| #10589345 | 2 |
| C3×#4482 | 2 |
| #10589090 | 2 |
| #71023 | 3 |
| #68470 | 3 |