Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
424 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 89 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. #11723094 | C2 | semidirect |
| 4. #11723093 | C2 | semidirect |
| 10. C2×C33×C8 | C4 | semidirect |
| 11. C2×C3×C3⋊(C3⋊C8) | C4 | semidirect |
| 12. C3×C8×C3⋊D3 | C4 | semidirect |
| 13. C3×C8×C3⋊D3 | C4 | semidirect |
| 41. C2×C32×C8 | Dic3 | semidirect |
| 42. C2×C3⋊(C3⋊C8) | Dic3 | semidirect |
| 43. C8×C3⋊D3 | Dic3 | semidirect |
| 44. C8×C3⋊D3 | Dic3 | semidirect |
| 106. C2×C3×C8 | #157 | semidirect |
| 139. C33 | #427 | semidirect |
| 182. C2×C8 | C3⋊#157 | semidirect |
| 208. C32 | #5106 | semidirect |
| 242. C3 | #10593768 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11724514 | 2 |
| C2×C3×C8×C3⋊D3 | 2 |
| #11723094 | 2 |
| #11723093 | 2 |
| #10593768 | 3 |
| #5106 | 9 |