Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
384 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 93. C3×Dic9 | Q16 | semidirect |
| 203. Dic9 | #216 | semidirect |
| 211. C3×C9 | #462 | semidirect |
| 297. C9 | #5031 | semidirect |
| 332. C3 | #10588862 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88547 | 2 |
| C3×Q8×Dic9 | 2 |
| C2×C9×#216 | 2 |
| #11720924 | 2 |
| #11720297 | 2 |
| #11720277 | 2 |
| Dic9⋊(C3⋊C8) | 2 |
| #10591625 | 3 |
| #10588862 | 3 |