Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
318 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 318 conjugacy classes of subgroups — too many to draw. Only its 74 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×#3755 | C2 | semidirect |
| 2. C3×#944 | C2 | semidirect |
| 3. C2×C3×#215 | C2 | semidirect |
| 5. C2×#3717 | C2 | semidirect |
| 6. C2×#3715 | C2 | semidirect |
| 7. Dic3×C3⋊C8 | C2 | semidirect |
| 25. #944 | D3 | semidirect |
| 31. C2×#215 | D3 | semidirect |
| 53. C3⋊(C3⋊C8) | D4 | semidirect |
| 54. C3×C3⋊C8 | D4 | semidirect |
| 95. C3×Dic3 | SD16 | semidirect |
| 144. C3⋊C8 | #67 | semidirect |
| 187. Dic3 | #215 | semidirect |
| 188. C32 | #492 | semidirect |
| 228. C3 | #5085 | semidirect |
| 229. C3 | #5175 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#3755 | 2 |
| C3×#944 | 2 |
| C2×C3×#215 | 2 |
| #63911 | 2 |
| C2×#3717 | 2 |
| C2×#3715 | 2 |
| Dic3×C3⋊C8 | 2 |
| #5175 | 3 |
| #5085 | 3 |