Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
273 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 273 conjugacy classes of subgroups — too many to draw. Only its 76 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×#3710 | C2 | semidirect |
| 4. #63647 | C2 | semidirect |
| 5. C3×Dic3⋊C8 | C2 | semidirect |
| 6. (C2×D3)⋊(C3⋊C8) | C2 | semidirect |
| 7. #63554 | C2 | semidirect |
| 25. C2×ΓL(1,𝔽25) | D3 | semidirect |
| 36. Dic3⋊C8 | D3 | semidirect |
| 53. C3×C3⋊C8 | D4 | semidirect |
| 87. C2×C3⋊D3 | M16 | semidirect |
| 142. C3⋊C8 | #67 | semidirect |
| 194. C32 | #435 | semidirect |
| 239. C3 | #4836 | semidirect |
| 240. 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×#626 | 2 |
| C2×#3710 | 2 |
| #63647 | 2 |
| C3×Dic3⋊C8 | 2 |
| (C2×D3)⋊(C3⋊C8) | 2 |
| #63554 | 2 |
| #5127 | 3 |
| #4836 | 3 |