Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
412 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 412 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 |
|---|---|---|
| 2. C3×#63488 | C2 | semidirect |
| 3. C9×#830 | C2 | semidirect |
| 4. #11720284 | C2 | semidirect |
| 5. #11720284 | C2 | semidirect |
| 6. #11720279 | C2 | semidirect |
| 7. #11720278 | C2 | semidirect |
| 30. #63488 | D3 | semidirect |
| 98. #830 | D9 | semidirect |
| 222. C3×C9 | #482 | semidirect |
| 326. C9 | #5003 | semidirect |
| 370. C3 | #10588419 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11721819 | 2 |
| C3×#63488 | 2 |
| C9×#830 | 2 |
| #11720284 | 2 |
| #11720279 | 2 |
| #11720278 | 2 |
| #10591136 | 3 |
| #10588419 | 3 |