Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
480 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 155 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 |
|---|---|---|
| 36. C3×Q8×C9 | Q8 | semidirect |
| 107. Q8×C9 | Dic6 | semidirect |
| 169. C3×C9 | #477 | semidirect |
| 172. C3×Q8 | Dic18 | semidirect |
| 230. C9 | #4793 | semidirect |
| 233. Q8 | #6226 | semidirect |
| 258. C3 | #10588473 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×C3⋊Dic9 | 2 |
| #11721744 | 2 |
| C3×C9×#103 | 2 |
| #11720582 | 2 |
| #11720541 | 2 |
| #11720537 | 2 |
| #11720525 | 2 |
| #10592492 | 3 |
| #10588473 | 3 |