Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
425 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 425 conjugacy classes of subgroups — too many to draw. Only its 100 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. #10591116 | C2 | semidirect |
| 5. #10589399 | C2 | semidirect |
| 6. C3×#4531 | C2 | semidirect |
| 7. #10589166 | C2 | semidirect |
| 37. #4531 | D3 | semidirect |
| 338. C32 | #2080 | semidirect |
| 390. C3 | #68700 | semidirect |
| 391. C3 | #70294 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#5002 | 2 |
| #10591116 | 2 |
| #10591111 | 2 |
| #10591076 | 2 |
| #10589399 | 2 |
| C3×#4531 | 2 |
| #10589166 | 2 |
| #70294 | 3 |
| #68700 | 3 |