Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
396 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 85 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×#88521 | C2 | semidirect |
| 3. #11720912 | C2 | semidirect |
| 6. C9×Dic3⋊C8 | C2 | semidirect |
| 7. #11720277 | C2 | semidirect |
| 109. Dic3⋊C8 | D9 | semidirect |
| 218. C3×C9 | #464 | semidirect |
| 310. C9 | #4767 | semidirect |
| 349. C3 | #10588529 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88521 | 2 |
| #11720948 | 2 |
| #11720912 | 2 |
| C2×#88415 | 2 |
| C3×#63380 | 2 |
| C9×Dic3⋊C8 | 2 |
| #11720277 | 2 |
| #10590861 | 3 |
| #10588529 | 3 |