Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
424 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 84 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. #10592540 | C2 | semidirect |
| 3. #10590327 | C2 | semidirect |
| 4. #10590273 | C2 | semidirect |
| 5. C3×#4485 | C2 | semidirect |
| 6. C3×#4479 | C2 | semidirect |
| 7. #10589094 | C2 | semidirect |
| 37. #4485 | D3 | semidirect |
| 39. #4479 | D3 | semidirect |
| 324. C32 | #1681 | semidirect |
| 377. C3 | #68397 | semidirect |
| 378. C3 | #68580 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592540 | 2 |
| #10590355 | 2 |
| #10590327 | 2 |
| #10590273 | 2 |
| C3×#4485 | 2 |
| C3×#4479 | 2 |
| #10589094 | 2 |
| #68580 | 3 |
| #68397 | 3 |