Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
568 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 113 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. C22×C9×Dic6 | C2 | semidirect |
| 3. C2×#88426 | C2 | semidirect |
| 4. C3×#63389 | C2 | semidirect |
| 5. #11720298 | C2 | semidirect |
| 29. #63389 | D3 | semidirect |
| 42. C9×Dic6 | D4 | semidirect |
| 75. C22×C3×C9 | SD16 | semidirect |
| 85. C22×Dic6 | D9 | semidirect |
| 181. C22×C9 | #204 | semidirect |
| 201. C3×C9 | #448 | semidirect |
| 235. Dic6 | #611 | semidirect |
| 272. C22×C3 | #3675 | semidirect |
| 298. C9 | #4738 | semidirect |
| 333. C22 | #88426 | semidirect |
| 340. C3 | #10588908 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C9×Dic6 | 2 |
| #11721819 | 2 |
| C2×#88426 | 2 |
| C3×#63389 | 2 |
| #11720298 | 2 |
| #10591174 | 3 |
| #10588908 | 3 |