Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
458 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 133 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 |
|---|---|---|
| 4. C8×C9×Dic3 | C2 | semidirect |
| 5. C3×#63375 | C2 | semidirect |
| 6. C3⋊C8×Dic9 | C2 | semidirect |
| 7. #11720258 | C2 | semidirect |
| 13. #88523 | C4 | semidirect |
| 20. (C3⋊D9)⋊C8 | C4 | semidirect |
| 33. #63375 | D3 | semidirect |
| 95. C8×Dic3 | D9 | semidirect |
| 186. C3×C9 | #405 | semidirect |
| 260. C9 | #4708 | semidirect |
| 290. C3 | #10588371 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88523 | 2 |
| #11720931 | 2 |
| C2×(C3⋊D9)⋊C8 | 2 |
| C8×C9×Dic3 | 2 |
| C3×#63375 | 2 |
| C3⋊C8×Dic9 | 2 |
| #11720258 | 2 |
| #10590910 | 3 |
| #10588371 | 3 |