Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
515 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 515 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 |
|---|---|---|
| 1. #10593951 | C2 | semidirect |
| 3. #10590377 | C2 | semidirect |
| 4. #10590364 | C2 | semidirect |
| 5. #10589322 | C2 | semidirect |
| 6. C3×#4456 | C2 | semidirect |
| 7. #10589090 | C2 | semidirect |
| 41. #4456 | D3 | semidirect |
| 362. C32 | #1620 | semidirect |
| 420. C3 | #68258 | semidirect |
| 421. C3 | #71284 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10593951 | 2 |
| C3×#4695 | 2 |
| #10590377 | 2 |
| #10590364 | 2 |
| #10589322 | 2 |
| C3×#4456 | 2 |
| #10589090 | 2 |
| #71284 | 3 |
| #68258 | 3 |