Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
333 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 333 conjugacy classes of subgroups — too many to draw. Only its 76 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. C2×#63627 | C2 | semidirect |
| 2. C3×#4901 | C2 | semidirect |
| 3. #10590932 | C2 | semidirect |
| 5. C3×#4506 | C2 | semidirect |
| 6. #10589131 | C2 | semidirect |
| 7. #10589128 | C2 | semidirect |
| 31. #4901 | D3 | semidirect |
| 37. #4506 | D3 | semidirect |
| 278. C32 | #2223 | semidirect |
| 315. C3 | #69363 | semidirect |
| 316. C3 | #71455 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#63627 | 2 |
| C3×#4901 | 2 |
| #10590932 | 2 |
| #10590927 | 2 |
| C3×#4506 | 2 |
| #10589131 | 2 |
| #10589128 | 2 |
| #71455 | 3 |
| #69363 | 3 |