Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
263 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 263 conjugacy classes of subgroups — too many to draw. Only its 106 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 |
| 3. C32×C4⋊C8 | C2 | semidirect |
| 4. C3×(C2×D3)⋊C8 | C2 | semidirect |
| 5. C3×C4×C3⋊C8 | C2 | semidirect |
| 7. #4838 | C3 | direct (N × H) |
| 19. C2×ΓL(1,𝔽25) | C2×C3 | semidirect |
| 22. C3×C4⋊C8 | D3 | semidirect |
| 23. C3×C4⋊C8 | C2×C3 | semidirect |
| 26. (C2×D3)⋊C8 | C2×C3 | semidirect |
| 27. C4×C3⋊C8 | C2×C3 | semidirect |
| 38. C3×C3⋊C8 | D4 | semidirect |
| 65. C32×C4 | M16 | semidirect |
| 71. C4⋊C8 | C3×D3 | semidirect |
| 99. C3⋊C8 | C3×D4 | semidirect |
| 129. C3×C4 | ΓL(1,𝔽25) | semidirect |
| 130. C3×C4 | C3×M16 | semidirect |
| 136. C32 | #436 | semidirect |
| 165. C4 | C3×ΓL(1,𝔽25) | semidirect |
| 169. C3 | #4838 | direct (N × H) |
| 170. C3 | C3×#436 | 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 |
| C3×C4×D12 | 2 |
| C32×C4⋊C8 | 2 |
| C3×(C2×D3)⋊C8 | 2 |
| C3×C4×C3⋊C8 | 2 |
| C3×#436 | 3 |
| #4838 | 3 |