Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
378 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 378 conjugacy classes of subgroups — too many to draw. Only its 121 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 |
|---|---|---|
| 3. #11720541 | C2 | semidirect |
| 4. C9×#818 | C2 | semidirect |
| 5. #11720264 | C2 | semidirect |
| 13. C3×C8×D9 | C4 | semidirect |
| 55. C8×D9 | Dic3 | semidirect |
| 73. #818 | D9 | semidirect |
| 147. C3×C9 | #427 | semidirect |
| 212. C9 | #5106 | semidirect |
| 243. C3 | #10588560 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C8×D9 | 2 |
| #11720907 | 2 |
| #11720541 | 2 |
| C9×#818 | 2 |
| #11720264 | 2 |
| #10590707 | 3 |
| #10588560 | 3 |