Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
293 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 293 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. D4×C9×A4 | C2 | semidirect |
| 2. C9×C4⋊S4 | C2 | semidirect |
| 3. C9×A4⋊C8 | C2 | semidirect |
| 13. C22×D4×C9 | D3 | semidirect |
| 27. #5415 | C9 | direct (N × H) |
| 51. C9×A4 | D8 | semidirect |
| 55. D4×A4 | C2×C9 | semidirect |
| 56. C4⋊S4 | C2×C9 | semidirect |
| 60. A4⋊C8 | C2×C9 | semidirect |
| 86. D4×C9 | S4 | semidirect |
| 132. C22×C9 | #213 | semidirect |
| 138. C22×D4 | D3×C9 | semidirect |
| 215. A4 | C9×D8 | semidirect |
| 223. C9 | #5415 | direct (N × H) |
| 237. D4 | C9×S4 | semidirect |
| 265. C22 | C9×#213 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×C9×A4 | 2 |
| C9×C4⋊S4 | 2 |
| C9×A4⋊C8 | 2 |
| C3×#5415 | 3 |
| C9×#447 | 3 |
| C9×#213 | 4 |