Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
285 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 285 conjugacy classes of subgroups — too many to draw. Only its 64 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. #63909 | C2 | semidirect |
| 3. #63908 | C2 | semidirect |
| 4. C2×#3714 | C2 | semidirect |
| 5. #63648 | C2 | semidirect |
| 6. C3×#821 | C2 | semidirect |
| 7. #63573 | C2 | semidirect |
| 29. C2×ΓL(1,𝔽25) | D3 | semidirect |
| 35. #821 | D3 | semidirect |
| 54. C3×C3⋊C8 | D4 | semidirect |
| 146. C3⋊C8 | #67 | semidirect |
| 203. C32 | #469 | semidirect |
| 253. C3 | #4782 | semidirect |
| 254. C3 | #5135 | 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 |
| #63909 | 2 |
| #63908 | 2 |
| C2×#3714 | 2 |
| #63648 | 2 |
| C3×#821 | 2 |
| #63573 | 2 |
| #5135 | 3 |
| #4782 | 3 |