Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
363 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 363 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. C3×#4908 | C2 | semidirect |
| 2. C3×#4700 | C2 | semidirect |
| 3. C3×#4695 | C2 | semidirect |
| 4. C32×#364 | C2 | semidirect |
| 5. C3×#4516 | C2 | semidirect |
| 7. #69305 | C3 | direct (N × H) |
| 22. #4908 | C2×C3 | semidirect |
| 23. #4700 | C2×C3 | semidirect |
| 24. #4695 | C2×C3 | semidirect |
| 26. C3×#364 | D3 | semidirect |
| 27. C3×#364 | C2×C3 | semidirect |
| 29. #4516 | C2×C3 | semidirect |
| 37. C3×Dic12 | D4 | semidirect |
| 42. C3×D24 | D4 | semidirect |
| 90. #364 | C3×D3 | semidirect |
| 118. Dic12 | C3×D4 | semidirect |
| 123. D24 | C3×D4 | semidirect |
| 226. C32 | #2213 | semidirect |
| 261. C3 | #69305 | direct (N × H) |
| 262. C3 | C3×#2213 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4908 | 2 |
| C3×#4700 | 2 |
| C3×#4695 | 2 |
| C32×#364 | 2 |
| C3×#4516 | 2 |
| C3×#2213 | 3 |
| #69305 | 3 |