Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
394 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 394 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. #88428 | C4 | semidirect |
| 203. C3×C9 | #441 | semidirect |
| 285. C9 | #4716 | semidirect |
| 318. C3 | #10588706 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#6226 | 2 |
| C4×C9×Dic6 | 2 |
| C2×#88428 | 2 |
| C3×#63362 | 2 |
| #11720298 | 2 |
| #11720269 | 2 |
| #11720264 | 2 |
| #10590383 | 3 |
| #10588706 | 3 |