Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
565 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 565 conjugacy classes of subgroups — too many to draw. Only its 122 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. C32×#493 | C2 | semidirect |
| 2. C3×#5076 | C2 | semidirect |
| 3. C3×#5073 | C2 | semidirect |
| 4. C3×#5073 | C2 | semidirect |
| 5. C3×#5070 | C2 | semidirect |
| 6. C3×#4694 | C2 | semidirect |
| 7. C3×#4454 | C2 | semidirect |
| 9. #71279 | C3 | direct (N × H) |
| 26. C3×#493 | D3 | semidirect |
| 27. C3×#493 | C2×C3 | semidirect |
| 31. #5076 | C2×C3 | semidirect |
| 32. #5073 | C2×C3 | semidirect |
| 33. #5073 | C2×C3 | semidirect |
| 34. #5070 | C2×C3 | semidirect |
| 35. #4694 | C2×C3 | semidirect |
| 37. #4454 | C2×C3 | semidirect |
| 108. C3×C3⋊C8 | D8 | semidirect |
| 111. #493 | C3×D3 | semidirect |
| 243. C3⋊C8 | C3×D8 | semidirect |
| 308. C32 | #1721 | semidirect |
| 361. C3 | #71279 | direct (N × H) |
| 362. C3 | C3×#1721 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#493 | 2 |
| C3×#5076 | 2 |
| C3×#5073 | 2 |
| C3×#5070 | 2 |
| C3×#4694 | 2 |
| C3×#4454 | 2 |
| C3×#1721 | 3 |
| #71279 | 3 |