Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
452 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 91 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. C2×#88524 | C2 | semidirect |
| 3. #11720912 | C2 | semidirect |
| 4. C2×#88415 | C2 | semidirect |
| 5. C3×#63380 | C2 | semidirect |
| 6. C9×Dic3⋊C8 | C2 | semidirect |
| 7. #11720284 | C2 | semidirect |
| 37. #63380 | D3 | semidirect |
| 45. #6226 | D4 | semidirect |
| 98. C9×Dic3 | SD16 | semidirect |
| 113. Dic3⋊C8 | D9 | semidirect |
| 233. C3×C9 | #460 | semidirect |
| 335. Dic3 | #3664 | semidirect |
| 338. C9 | #4762 | semidirect |
| 384. C3 | #10588512 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88524 | 2 |
| #11721006 | 2 |
| #11720912 | 2 |
| C2×#88415 | 2 |
| C3×#63380 | 2 |
| C9×Dic3⋊C8 | 2 |
| #11720284 | 2 |
| #10590879 | 3 |
| #10588512 | 3 |