Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
212 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 212 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×#97 | C2 | semidirect |
| 4. C3×Dic3⋊C8 | C2 | semidirect |
| 5. C3×C4×C3⋊C8 | C2 | semidirect |
| 7. #4709 | C3 | direct (N × H) |
| 20. C3×#97 | D3 | semidirect |
| 21. C3×#97 | C2×C3 | semidirect |
| 24. Dic3⋊C8 | C2×C3 | semidirect |
| 25. C4×C3⋊C8 | C2×C3 | semidirect |
| 61. #97 | C3×D3 | semidirect |
| 109. C32 | #433 | semidirect |
| 134. C3 | #4709 | direct (N × H) |
| 135. 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×#97 | 2 |
| C3×(C2×D3)⋊C8 | 2 |
| C3×Dic3⋊C8 | 2 |
| C3×C4×C3⋊C8 | 2 |
| C3×#433 | 3 |
| #4709 | 3 |