Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
346 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 95 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. C9×#812 | C2 | semidirect |
| 3. C3×#63371 | C2 | semidirect |
| 4. #11720231 | C2 | semidirect |
| 5. (C3⋊D9)⋊C16 | C2 | semidirect |
| 15. C9×C3⋊C16 | C22 | semidirect |
| 16. C3×C9⋊C16 | C22 | semidirect |
| 25. #63371 | D3 | semidirect |
| 65. C9⋊C16 | C2×D3 | semidirect |
| 80. #812 | D9 | semidirect |
| 122. C3⋊D9 | M32 | semidirect |
| 147. C3⋊C16 | C2×D9 | semidirect |
| 177. C3×C9 | C2×M32 | semidirect |
| 258. C9 | D3×M32 | semidirect |
| 291. C3 | D9×M32 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C8×C3⋊D9 | 2 |
| C9×#812 | 2 |
| C3×#63371 | 2 |
| #11720231 | 2 |
| (C3⋊D9)⋊C16 | 2 |
| #10590625 | 3 |
| D9×M32 | 3 |