Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
634 conjugacy classes of subgroups; only the 222 normal subgroups are shown.
This group has 634 conjugacy classes of subgroups — too many to draw. Only its 222 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×#235 | C2 | semidirect |
| 2. C2×C32×C4⋊C4 | C2 | semidirect |
| 3. C3×#930 | C2 | semidirect |
| 4. C3×#897 | C2 | semidirect |
| 5. C3×#895 | C2 | semidirect |
| 7. #5510 | C3 | direct (N × H) |
| 20. C2×#235 | C2×C3 | semidirect |
| 25. C2×C3×C4⋊C4 | D3 | semidirect |
| 26. C2×C3×C4⋊C4 | C2×C3 | semidirect |
| 27. #930 | C2×C3 | semidirect |
| 28. #897 | C2×C3 | semidirect |
| 29. #895 | C2×C3 | semidirect |
| 33. C2×C32×C4 | D4 | semidirect |
| 82. C2×C4⋊C4 | C3×D3 | semidirect |
| 100. C2×C3×C4 | D12 | semidirect |
| 101. C2×C3×C4 | C3×D4 | semidirect |
| 154. C32 | #537 | semidirect |
| 164. C2×C4 | C3×D12 | semidirect |
| 192. C3 | #5510 | direct (N × H) |
| 193. C3 | C3×#537 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#235 | 2 |
| C2×C32×C4⋊C4 | 2 |
| C3×#930 | 2 |
| C3×#897 | 2 |
| C3×#895 | 2 |
| C3×#537 | 3 |
| #5510 | 3 |