Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
299 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 299 conjugacy classes of subgroups — too many to draw. Only its 82 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. C3×#4893 | C2 | semidirect |
| 3. C32×#361 | C2 | semidirect |
| 4. C3×#4563 | C2 | semidirect |
| 5. C3×#4514 | C2 | semidirect |
| 6. C3×#4513 | C2 | semidirect |
| 7. C3×#4494 | C2 | semidirect |
| 9. #69257 | C3 | direct (N × H) |
| 24. #4893 | C2×C3 | semidirect |
| 29. C3×#361 | D3 | semidirect |
| 30. C3×#361 | C2×C3 | semidirect |
| 32. #4563 | C2×C3 | semidirect |
| 33. #4514 | C2×C3 | semidirect |
| 34. #4513 | C2×C3 | semidirect |
| 35. #4494 | C2×C3 | semidirect |
| 99. #361 | C3×D3 | semidirect |
| 246. C32 | #2238 | semidirect |
| 284. C3 | #69257 | direct (N × H) |
| 285. C3 | C3×#2238 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#5159 | 2 |
| C3×#4893 | 2 |
| C32×#361 | 2 |
| C3×#4563 | 2 |
| C3×#4514 | 2 |
| C3×#4513 | 2 |
| C3×#4494 | 2 |
| C3×#2238 | 3 |
| #69257 | 3 |