Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
298 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 82 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×C32×D8 | C2 | semidirect |
| 2. C3×#938 | C2 | semidirect |
| 3. C2×C3×ΓL(1,𝔽25) | C2 | semidirect |
| 4. C3×#832 | C2 | semidirect |
| 5. C3×#817 | C2 | semidirect |
| 7. #5159 | C3 | direct (N × H) |
| 18. C2×C3×D8 | D3 | semidirect |
| 19. C2×C3×D8 | C2×C3 | semidirect |
| 22. #938 | C2×C3 | semidirect |
| 23. C2×ΓL(1,𝔽25) | C2×C3 | semidirect |
| 26. #832 | C2×C3 | semidirect |
| 27. #817 | C2×C3 | semidirect |
| 38. C32×C8 | D4 | semidirect |
| 72. C2×D8 | C3×D3 | semidirect |
| 103. C3×C8 | #67 | semidirect |
| 104. C3×C8 | C3×D4 | semidirect |
| 145. C32 | #469 | semidirect |
| 157. C8 | C3×#67 | semidirect |
| 180. C3 | #5159 | direct (N × H) |
| 181. C3 | C3×#469 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×D8 | 2 |
| C3×#938 | 2 |
| C2×C3×ΓL(1,𝔽25) | 2 |
| C3×#832 | 2 |
| C3×#817 | 2 |
| C3×#469 | 3 |
| #5159 | 3 |