Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
467 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 467 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×#5699 | C2 | semidirect |
| 2. C32×#490 | C2 | semidirect |
| 4. C3×#5071 | C2 | semidirect |
| 5. C3×#4543 | C2 | semidirect |
| 6. C3×#4465 | C2 | semidirect |
| 7. C3×#4464 | C2 | semidirect |
| 9. #71249 | C3 | direct (N × H) |
| 30. #5699 | C2×C3 | semidirect |
| 34. C3×#490 | D3 | semidirect |
| 35. C3×#490 | C2×C3 | semidirect |
| 37. #5071 | C2×C3 | semidirect |
| 41. #4543 | C2×C3 | semidirect |
| 42. #4465 | C2×C3 | semidirect |
| 43. #4464 | C2×C3 | semidirect |
| 141. #490 | C3×D3 | semidirect |
| 372. C32 | #1657 | semidirect |
| 424. C3 | #71249 | direct (N × H) |
| 425. C3 | C3×#1657 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#5699 | 2 |
| C32×#490 | 2 |
| C3×#5074 | 2 |
| C3×#5071 | 2 |
| C3×#4543 | 2 |
| C3×#4465 | 2 |
| C3×#4464 | 2 |
| C3×#1657 | 3 |
| #71249 | 3 |