Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
261 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 261 conjugacy classes of subgroups — too many to draw. Only its 78 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×#946 | C2 | semidirect |
| 2. C2×C3×#215 | C2 | semidirect |
| 3. C2×C3×ΓL(1,𝔽25) | C2 | semidirect |
| 5. C32×#103 | C2 | semidirect |
| 6. C3×#821 | C2 | semidirect |
| 7. C3×#807 | C2 | semidirect |
| 9. #4812 | C3 | direct (N × H) |
| 27. #946 | C2×C3 | semidirect |
| 28. C2×#215 | C2×C3 | semidirect |
| 29. C2×ΓL(1,𝔽25) | C2×C3 | semidirect |
| 33. C3×#103 | D3 | semidirect |
| 34. C3×#103 | C2×C3 | semidirect |
| 36. #821 | C2×C3 | semidirect |
| 37. #807 | C2×C3 | semidirect |
| 53. C3×C3⋊C8 | D4 | semidirect |
| 102. #103 | C3×D3 | semidirect |
| 141. C3⋊C8 | C3×D4 | semidirect |
| 191. C32 | #468 | semidirect |
| 235. C3 | #4812 | direct (N × H) |
| 236. C3 | C3×#468 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#946 | 2 |
| C2×C3×#215 | 2 |
| C2×C3×ΓL(1,𝔽25) | 2 |
| C3×#895 | 2 |
| C32×#103 | 2 |
| C3×#821 | 2 |
| C3×#807 | 2 |
| C3×#468 | 3 |
| #4812 | 3 |