Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
232 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 51 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 |
|---|---|---|
| 2. C8×C9×A4 | C2 | semidirect |
| 3. C9×A4⋊C8 | C2 | semidirect |
| 14. C22×C8×C9 | D3 | semidirect |
| 26. #5400 | C9 | direct (N × H) |
| 47. C9×A4 | M16 | semidirect |
| 55. C8×A4 | C2×C9 | semidirect |
| 56. A4⋊C8 | C2×C9 | semidirect |
| 82. C8×C9 | S4 | semidirect |
| 113. C22×C9 | ΓL(1,𝔽25) | semidirect |
| 122. C22×C8 | D3×C9 | semidirect |
| 179. A4 | C9×M16 | semidirect |
| 190. C9 | #5400 | direct (N × H) |
| 205. C8 | C9×S4 | semidirect |
| 218. C22 | C9×ΓL(1,𝔽25) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C9×S4 | 2 |
| C8×C9×A4 | 2 |
| C9×A4⋊C8 | 2 |
| C3×#5400 | 3 |
| C9×#435 | 3 |
| C9×ΓL(1,𝔽25) | 4 |