Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
231 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 231 conjugacy classes of subgroups — too many to draw. Only its 74 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×#908 | C2 | semidirect |
| 2. C2×C3×D24 | C2 | semidirect |
| 3. C3×#901 | C2 | semidirect |
| 4. C32×#108 | C2 | semidirect |
| 5. C3×#823 | C2 | semidirect |
| 7. #4897 | C3 | direct (N × H) |
| 22. #908 | C2×C3 | semidirect |
| 23. C2×D24 | C2×C3 | semidirect |
| 24. #901 | C2×C3 | semidirect |
| 26. C3×#108 | D3 | semidirect |
| 27. C3×#108 | C2×C3 | semidirect |
| 29. #823 | C2×C3 | semidirect |
| 77. #108 | C3×D3 | semidirect |
| 139. C32 | #472 | semidirect |
| 170. C3 | #4897 | direct (N × H) |
| 171. C3 | C3×#472 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#908 | 2 |
| C2×C3×D24 | 2 |
| C3×#901 | 2 |
| C32×#108 | 2 |
| C3×#823 | 2 |
| C3×#472 | 3 |
| #4897 | 3 |