Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
282 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 282 conjugacy classes of subgroups — too many to draw. Only its 55 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 |
|---|---|---|
| 52. C9×A4 | Q16 | semidirect |
| 115. C22×C9 | #216 | semidirect |
| 116. C22⋊C9 | #216 | semidirect |
| 175. A4 | #3674 | semidirect |
| 187. C9 | #5416 | semidirect |
| 209. C22 | #88547 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×C9×A4 | 2 |
| #11722366 | 2 |
| C9⋊(A4⋊C8) | 2 |
| #10593650 | 3 |
| #10589518 | 3 |
| #10588907 | 3 |
| #88547 | 4 |