Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
285 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 285 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×#938 | C2 | semidirect |
| 2. C2×C3×#213 | C2 | semidirect |
| 3. C2×C3×ΓL(1,𝔽25) | C2 | semidirect |
| 4. C3×#895 | C2 | semidirect |
| 5. C32×#102 | C2 | semidirect |
| 6. C3×#821 | C2 | semidirect |
| 7. C3×#808 | C2 | semidirect |
| 9. #4782 | C3 | direct (N × H) |
| 27. #938 | C2×C3 | semidirect |
| 28. C2×#213 | C2×C3 | semidirect |
| 29. C2×ΓL(1,𝔽25) | C2×C3 | semidirect |
| 30. #895 | C2×C3 | semidirect |
| 34. C3×#102 | D3 | semidirect |
| 35. C3×#102 | C2×C3 | semidirect |
| 36. #821 | C2×C3 | semidirect |
| 37. #808 | C2×C3 | semidirect |
| 54. C3×C3⋊C8 | D4 | semidirect |
| 106. #102 | C3×D3 | semidirect |
| 146. C3⋊C8 | C3×D4 | semidirect |
| 203. C32 | #469 | semidirect |
| 253. C3 | #4782 | direct (N × H) |
| 254. C3 | C3×#469 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#938 | 2 |
| C2×C3×#213 | 2 |
| C2×C3×ΓL(1,𝔽25) | 2 |
| C3×#895 | 2 |
| C32×#102 | 2 |
| C3×#821 | 2 |
| C3×#808 | 2 |
| C3×#469 | 3 |
| #4782 | 3 |