Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
488 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 97 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×M16×D9 | C2 | semidirect |
| 3. D9×#208 | C2 | semidirect |
| 4. #11720556 | C2 | semidirect |
| 5. C9×#823 | C2 | semidirect |
| 6. #11720296 | C2 | semidirect |
| 7. #11720290 | C2 | semidirect |
| 36. M16×D9 | D3 | semidirect |
| 127. #823 | D9 | semidirect |
| 252. C3×C9 | #413 | semidirect |
| 358. C9 | #5132 | semidirect |
| 404. C3 | #10588425 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88638 | 2 |
| C3×M16×D9 | 2 |
| D9×#208 | 2 |
| #11720556 | 2 |
| C9×#823 | 2 |
| #11720296 | 2 |
| #11720290 | 2 |
| #10591006 | 3 |
| #10588425 | 3 |