Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
393 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 393 conjugacy classes of subgroups — too many to draw. Only its 98 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×#443 | C2 | semidirect |
| 2. C3×#5193 | C2 | semidirect |
| 3. C3×#4695 | C2 | semidirect |
| 4. C3×#4495 | C2 | semidirect |
| 5. C3×#4463 | C2 | semidirect |
| 7. #70926 | C3 | direct (N × H) |
| 22. C3×#443 | D3 | semidirect |
| 23. C3×#443 | C2×C3 | semidirect |
| 24. #5193 | C2×C3 | semidirect |
| 25. #4695 | C2×C3 | semidirect |
| 28. #4495 | C2×C3 | semidirect |
| 29. #4463 | C2×C3 | semidirect |
| 33. C32×Q16 | D4 | semidirect |
| 35. C32×D8 | D4 | semidirect |
| 92. #443 | C3×D3 | semidirect |
| 103. C3×Q16 | D12 | semidirect |
| 104. C3×Q16 | C3×D4 | semidirect |
| 113. C3×D8 | D12 | semidirect |
| 114. C3×D8 | C3×D4 | semidirect |
| 206. Q16 | C3×D12 | semidirect |
| 212. D8 | C3×D12 | semidirect |
| 242. C32 | #2213 | semidirect |
| 278. C3 | #70926 | direct (N × H) |
| 279. C3 | C3×#2213 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#443 | 2 |
| C3×#5193 | 2 |
| C3×#4695 | 2 |
| C3×#4495 | 2 |
| C3×#4463 | 2 |
| C3×#2213 | 3 |
| #70926 | 3 |