Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
453 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 453 conjugacy classes of subgroups — too many to draw. Only its 94 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. C32×#510 | C2 | semidirect |
| 3. C3×#5192 | C2 | semidirect |
| 4. C2×C3×#829 | C2 | semidirect |
| 5. C3×#4567 | C2 | semidirect |
| 6. C3×#4517 | C2 | semidirect |
| 7. C3×#4515 | C2 | semidirect |
| 9. #71524 | C3 | direct (N × H) |
| 30. C3×#510 | D3 | semidirect |
| 31. C3×#510 | C2×C3 | semidirect |
| 34. #5192 | C2×C3 | semidirect |
| 35. C2×#829 | C2×C3 | semidirect |
| 39. #4567 | C2×C3 | semidirect |
| 40. #4517 | C2×C3 | semidirect |
| 41. #4515 | C2×C3 | semidirect |
| 133. #510 | C3×D3 | semidirect |
| 339. C32 | #2195 | semidirect |
| 384. C3 | #71524 | direct (N × H) |
| 385. C3 | C3×#2195 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#5771 | 2 |
| C32×#510 | 2 |
| C3×#5192 | 2 |
| C2×C3×#829 | 2 |
| C3×#4567 | 2 |
| C3×#4517 | 2 |
| C3×#4515 | 2 |
| C3×#2195 | 3 |
| #71524 | 3 |