Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
364 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 21. #88427 | C4 | semidirect |
| 195. C3×C9 | #441 | semidirect |
| 273. C9 | #5030 | semidirect |
| 306. C3 | #10588706 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C9×Dic6 | 2 |
| C3×C4×Dic18 | 2 |
| C2×#88427 | 2 |
| #11720516 | 2 |
| #11720297 | 2 |
| #11720268 | 2 |
| #11720265 | 2 |
| #10590381 | 3 |
| #10588706 | 3 |