Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
554 conjugacy classes of subgroups; only the 164 normal subgroups are shown.
This group has 554 conjugacy classes of subgroups — too many to draw. Only its 164 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 |
|---|---|---|
| 3. C2×Dic32 | C2 | semidirect |
| 4. #63658 | C2 | semidirect |
| 5. C3×C3⋊#95 | C2 | semidirect |
| 14. C2×C3×C4×D3 | C4 | semidirect |
| 15. (C2×D3)⋊Dic3 | C4 | semidirect |
| 27. C3⋊#95 | D3 | semidirect |
| 38. C2×C3⋊Dic3 | C2×C4 | semidirect |
| 42. C2×C3×Dic3 | C2×C4 | semidirect |
| 61. C2×C4×D3 | Dic3 | semidirect |
| 75. C2×C3×D3 | C42 | semidirect |
| 79. C3×Dic3 | C22⋊C4 | semidirect |
| 121. C2×Dic3 | C4×D3 | semidirect |
| 164. C2×D3 | C4×Dic3 | semidirect |
| 174. Dic3 | #217 | semidirect |
| 175. C32 | C4×C22⋊C4 | semidirect |
| 225. C3 | #4666 | semidirect |
| 226. C3 | C4×#217 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×C4×D3 | 2 |
| C2×(C2×D3)⋊Dic3 | 2 |
| C2×Dic32 | 2 |
| #63658 | 2 |
| C3×C3⋊#95 | 2 |
| C4×#217 | 3 |
| #4666 | 3 |