Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
518 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 518 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. M16×C3⋊D9 | C2 | semidirect |
| 3. #11720863 | C2 | semidirect |
| 4. C9×#823 | C2 | semidirect |
| 5. C3×#63382 | C2 | semidirect |
| 6. #11720296 | C2 | semidirect |
| 7. #11720289 | C2 | semidirect |
| 41. #63382 | D3 | semidirect |
| 129. #823 | D9 | semidirect |
| 263. C3×C9 | #413 | semidirect |
| 378. C9 | #4751 | semidirect |
| 426. C3 | #10588425 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88639 | 2 |
| M16×C3⋊D9 | 2 |
| #11720863 | 2 |
| C9×#823 | 2 |
| C3×#63382 | 2 |
| #11720296 | 2 |
| #11720289 | 2 |
| #10591010 | 3 |
| #10588425 | 3 |