Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
346 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 77 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×#88525 | C2 | semidirect |
| 2. C3×#63467 | C2 | semidirect |
| 3. C9×#812 | C2 | semidirect |
| 4. #11720234 | C2 | semidirect |
| 5. #11720232 | C2 | semidirect |
| 13. C3×D72 | C22 | semidirect |
| 15. C3×Dic36 | C22 | semidirect |
| 16. C9×C3⋊C16 | C22 | semidirect |
| 22. #63467 | D3 | semidirect |
| 58. D72 | C2×D3 | semidirect |
| 60. Dic36 | C2×D3 | semidirect |
| 77. #812 | D9 | semidirect |
| 132. C3⋊C16 | C2×D9 | semidirect |
| 157. C3×C9 | #509 | semidirect |
| 225. C9 | #5193 | semidirect |
| 255. C3 | #10588588 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88525 | 2 |
| C3×#63467 | 2 |
| C9×#812 | 2 |
| #11720234 | 2 |
| #11720232 | 2 |
| #10590634 | 3 |
| #10588588 | 3 |