Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
306 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 106 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. C22×C3⋊(C3⋊C8) | C2 | semidirect |
| 3. C2×D3×C3⋊C8 | C2 | semidirect |
| 4. C3×#830 | C2 | semidirect |
| 5. Dic3⋊(C3⋊C8) | C2 | semidirect |
| 6. (C2×D3)⋊(C3⋊C8) | C2 | semidirect |
| 7. Dic3×C3⋊C8 | C2 | semidirect |
| 32. #830 | D3 | semidirect |
| 44. C3×#67 | C8 | semidirect |
| 51. C3⋊(C3⋊C8) | D4 | semidirect |
| 87. C22×C32 | C2×C8 | semidirect |
| 91. C2×C3×D3 | C2×C8 | semidirect |
| 97. C3×Dic3 | C2×C8 | semidirect |
| 128. #67 | C3⋊C8 | semidirect |
| 173. C22×C3 | D3×C8 | semidirect |
| 174. C22×C3 | C2×C3⋊C8 | semidirect |
| 179. C2×D3 | C2×C3⋊C8 | semidirect |
| 194. Dic3 | C2×C3⋊C8 | semidirect |
| 195. C32 | C8×D4 | semidirect |
| 231. C22 | D3×C3⋊C8 | semidirect |
| 240. C3 | #67⋊C8 | semidirect |
| 241. C3 | D4×C3⋊C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3⋊(C3⋊C8) | 2 |
| C3×C4×#67 | 2 |
| C2×D3×C3⋊C8 | 2 |
| C3×#830 | 2 |
| Dic3⋊(C3⋊C8) | 2 |
| (C2×D3)⋊(C3⋊C8) | 2 |
| Dic3×C3⋊C8 | 2 |
| D4×C3⋊C8 | 3 |
| #67⋊C8 | 3 |