Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
360 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 83 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. C2×#88418 | C2 | semidirect |
| 5. #11720290 | C2 | semidirect |
| 6. #11720289 | C2 | semidirect |
| 7. #11720280 | C2 | semidirect |
| 222. C3×C9 | #473 | semidirect |
| 310. C9 | #5204 | semidirect |
| 344. C3 | #10588821 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11721866 | 2 |
| C3×#63511 | 2 |
| C9×#948 | 2 |
| C2×#88418 | 2 |
| #11720290 | 2 |
| #11720289 | 2 |
| #11720280 | 2 |
| #10591682 | 3 |
| #10588821 | 3 |