Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
267 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 267 conjugacy classes of subgroups — too many to draw. Only its 102 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. C2×C3×ΓL(1,𝔽25) | C2 | semidirect |
| 2. C2×C3×D3×C8 | C2 | semidirect |
| 4. C32×C4⋊C8 | C2 | semidirect |
| 5. C3×(C2×D3)⋊C8 | C2 | semidirect |
| 6. C3×(C2×D3)⋊C8 | C2 | semidirect |
| 7. C3×#803 | C2 | semidirect |
| 9. #4836 | C3 | direct (N × H) |
| 26. C2×ΓL(1,𝔽25) | C2×C3 | semidirect |
| 27. C2×D3×C8 | C2×C3 | semidirect |
| 30. C3×C4⋊C8 | D3 | semidirect |
| 31. C3×C4⋊C8 | C2×C3 | semidirect |
| 35. (C2×D3)⋊C8 | C2×C3 | semidirect |
| 36. (C2×D3)⋊C8 | C2×C3 | semidirect |
| 37. #803 | C2×C3 | semidirect |
| 53. C3×C3⋊C8 | D4 | semidirect |
| 90. C2×C3×D3 | M16 | semidirect |
| 100. C4⋊C8 | C3×D3 | semidirect |
| 140. C3⋊C8 | C3×D4 | semidirect |
| 173. C2×D3 | C3×M16 | semidirect |
| 190. C32 | #435 | semidirect |
| 234. C3 | #4836 | direct (N × H) |
| 235. C3 | C3×#435 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×ΓL(1,𝔽25) | 2 |
| C2×C3×D3×C8 | 2 |
| C3×C4×D12 | 2 |
| C32×C4⋊C8 | 2 |
| C3×(C2×D3)⋊C8 | 2 |
| C3×#803 | 2 |
| C3×#435 | 3 |
| #4836 | 3 |