Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
421 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 421 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 |
|---|---|---|
| 1. C32×#493 | C2 | semidirect |
| 2. C3×#5147 | C2 | semidirect |
| 3. C3×#4700 | C2 | semidirect |
| 4. C3×#4563 | C2 | semidirect |
| 5. C3×#4463 | C2 | semidirect |
| 7. #71295 | C3 | direct (N × H) |
| 21. C3×#493 | D3 | semidirect |
| 22. C3×#493 | C2×C3 | semidirect |
| 24. #5147 | C2×C3 | semidirect |
| 25. #4700 | C2×C3 | semidirect |
| 28. #4563 | C2×C3 | semidirect |
| 29. #4463 | C2×C3 | semidirect |
| 41. C3×Dic12 | D4 | semidirect |
| 42. C3×D24 | D4 | semidirect |
| 90. #493 | C3×D3 | semidirect |
| 130. Dic12 | C3×D4 | semidirect |
| 131. D24 | C3×D4 | semidirect |
| 239. C32 | #2213 | semidirect |
| 275. C3 | #71295 | direct (N × H) |
| 276. C3 | C3×#2213 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#493 | 2 |
| C3×#5147 | 2 |
| C3×#4700 | 2 |
| C3×#4563 | 2 |
| C3×#4463 | 2 |
| C3×#2213 | 3 |
| #71295 | 3 |