Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
211 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 211 conjugacy classes of subgroups — too many to draw. Only its 94 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 |
|---|---|---|
| 2. C32×C4⋊C8 | C2 | semidirect |
| 5. C3×#815 | C2 | semidirect |
| 6. C3×C8×Dic3 | C2 | semidirect |
| 7. C3×C4⋊(C3⋊C8) | C2 | semidirect |
| 9. #4840 | C3 | direct (N × H) |
| 25. C3×C4⋊C8 | D3 | semidirect |
| 26. C3×C4⋊C8 | C2×C3 | semidirect |
| 33. #815 | C2×C3 | semidirect |
| 34. C8×Dic3 | C2×C3 | semidirect |
| 35. C4⋊(C3⋊C8) | C2×C3 | semidirect |
| 88. C4⋊C8 | C3×D3 | semidirect |
| 166. C32 | #433 | semidirect |
| 203. C3 | #4840 | direct (N × H) |
| 204. C3 | C3×#433 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#872 | 2 |
| C32×C4⋊C8 | 2 |
| C3×(C2×D3)⋊C8 | 2 |
| C3×#815 | 2 |
| C3×C8×Dic3 | 2 |
| C3×C4⋊(C3⋊C8) | 2 |
| C3×#433 | 3 |
| #4840 | 3 |