Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
495 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 495 conjugacy classes of subgroups — too many to draw. Only its 90 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. C3×#5684 | C2 | semidirect |
| 2. C3×#5058 | C2 | semidirect |
| 3. C3×#4713 | C2 | semidirect |
| 4. C3×#4712 | C2 | semidirect |
| 5. C32×#329 | C2 | semidirect |
| 6. C3×#4465 | C2 | semidirect |
| 7. C3×#4464 | C2 | semidirect |
| 9. #68351 | C3 | direct (N × H) |
| 30. #5684 | C2×C3 | semidirect |
| 34. #5058 | C2×C3 | semidirect |
| 35. #4713 | C2×C3 | semidirect |
| 36. #4712 | C2×C3 | semidirect |
| 40. C3×#329 | D3 | semidirect |
| 41. C3×#329 | C2×C3 | semidirect |
| 42. #4465 | C2×C3 | semidirect |
| 43. #4464 | C2×C3 | semidirect |
| 149. #329 | C3×D3 | semidirect |
| 395. C32 | #1656 | semidirect |
| 456. C3 | #68351 | direct (N × H) |
| 457. C3 | C3×#1656 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#5684 | 2 |
| C3×#5058 | 2 |
| C3×#4713 | 2 |
| C3×#4712 | 2 |
| C32×#329 | 2 |
| C3×#4465 | 2 |
| C3×#4464 | 2 |
| C3×#1656 | 3 |
| #68351 | 3 |