Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
267 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 267 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. C2×C3×ΓL(1,𝔽25) | C2 | semidirect |
| 3. C2×D3×C3⋊C8 | C2 | semidirect |
| 4. #63641 | C2 | semidirect |
| 5. C3×(C2×D3)⋊C8 | C2 | semidirect |
| 6. (C2×D3)⋊(C3⋊C8) | C2 | semidirect |
| 7. #63555 | C2 | semidirect |
| 27. C2×ΓL(1,𝔽25) | D3 | semidirect |
| 32. (C2×D3)⋊C8 | D3 | semidirect |
| 53. C3×C3⋊C8 | D4 | semidirect |
| 90. C2×C3×D3 | M16 | semidirect |
| 140. C3⋊C8 | #67 | semidirect |
| 173. C2×D3 | ΓL(1,𝔽25) | semidirect |
| 190. C32 | #435 | semidirect |
| 234. C3 | #4730 | semidirect |
| 235. C3 | #5127 | 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 |
| C4×#625 | 2 |
| C2×D3×C3⋊C8 | 2 |
| #63641 | 2 |
| C3×(C2×D3)⋊C8 | 2 |
| (C2×D3)⋊(C3⋊C8) | 2 |
| #63555 | 2 |
| #5127 | 3 |
| #4730 | 3 |