Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
385 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 385 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. C32×#509 | C2 | semidirect |
| 2. C3×#5196 | C2 | semidirect |
| 3. C3×#5193 | C2 | semidirect |
| 4. C3×#5151 | C2 | semidirect |
| 5. C3×#4563 | C2 | semidirect |
| 6. C3×#4516 | C2 | semidirect |
| 7. C3×#4511 | C2 | semidirect |
| 9. #71514 | C3 | direct (N × H) |
| 27. C3×#509 | D3 | semidirect |
| 28. C3×#509 | C2×C3 | semidirect |
| 31. #5196 | C2×C3 | semidirect |
| 32. #5193 | C2×C3 | semidirect |
| 33. #5151 | C2×C3 | semidirect |
| 37. #4563 | C2×C3 | semidirect |
| 38. #4516 | C2×C3 | semidirect |
| 39. #4511 | C2×C3 | semidirect |
| 44. C32×Q16 | D4 | semidirect |
| 48. C32×D8 | D4 | semidirect |
| 116. #509 | C3×D3 | semidirect |
| 133. C3×Q16 | #67 | semidirect |
| 134. C3×Q16 | C3×D4 | semidirect |
| 149. C3×D8 | #67 | semidirect |
| 150. C3×D8 | C3×D4 | semidirect |
| 253. Q16 | C3×#67 | semidirect |
| 261. D8 | C3×#67 | semidirect |
| 297. C32 | #2213 | semidirect |
| 341. C3 | #71514 | direct (N × H) |
| 342. C3 | C3×#2213 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#509 | 2 |
| C3×#5196 | 2 |
| C3×#5193 | 2 |
| C3×#5151 | 2 |
| C3×#4563 | 2 |
| C3×#4516 | 2 |
| C3×#4511 | 2 |
| C3×#2213 | 3 |
| #71514 | 3 |