Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
255 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 255 conjugacy classes of subgroups — too many to draw. Only its 45 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 |
|---|---|---|
| 1. Q8×C9×A4 | C2 | semidirect |
| 3. C9×A4⋊C8 | C2 | semidirect |
| 13. C22×Q8×C9 | D3 | semidirect |
| 26. #5417 | C9 | direct (N × H) |
| 49. C9×A4 | SD16 | semidirect |
| 54. Q8×A4 | C2×C9 | semidirect |
| 59. A4⋊C8 | C2×C9 | semidirect |
| 75. Q8×C9 | S4 | semidirect |
| 119. C22×C9 | #215 | semidirect |
| 128. C22×Q8 | D3×C9 | semidirect |
| 189. A4 | C9×SD16 | semidirect |
| 201. C9 | #5417 | direct (N × H) |
| 207. Q8 | C9×S4 | semidirect |
| 231. C22 | C9×#215 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×C9×A4 | 2 |
| C9×C4⋊S4 | 2 |
| C9×A4⋊C8 | 2 |
| C3×#5417 | 3 |
| C9×#448 | 3 |
| C9×#215 | 4 |