Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
352 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 352 conjugacy classes of subgroups — too many to draw. Only its 83 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. #11720878 | C2 | semidirect |
| 3. #11720859 | C2 | semidirect |
| 4. #11720516 | C2 | semidirect |
| 5. C9×#805 | C2 | semidirect |
| 6. C3×#63364 | C2 | semidirect |
| 7. #11720286 | C2 | semidirect |
| 17. #88427 | C4 | semidirect |
| 18. #88425 | C4 | semidirect |
| 19. #88423 | C4 | semidirect |
| 20. #88421 | C4 | semidirect |
| 37. #63364 | D3 | semidirect |
| 110. #805 | D9 | semidirect |
| 217. C3×C9 | #444 | semidirect |
| 303. C9 | #4823 | semidirect |
| 339. C3 | #10588503 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11720881 | 2 |
| #11720878 | 2 |
| #11720859 | 2 |
| #11720516 | 2 |
| C9×#805 | 2 |
| C3×#63364 | 2 |
| #11720286 | 2 |
| #10590390 | 3 |
| #10588503 | 3 |