Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
226 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 226 conjugacy classes of subgroups — too many to draw. Only its 79 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. C2×C3⋊(C9⋊C16) | C2 | semidirect |
| 3. C3×#63378 | C2 | semidirect |
| 10. C9×D24 | C4 | semidirect |
| 16. #63378 | D3 | semidirect |
| 88. D24 | Dic9 | semidirect |
| 112. C3×C9 | #357 | semidirect |
| 166. C9 | #4491 | semidirect |
| 193. C3 | #10588239 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C9×D24 | 2 |
| C2×C3⋊(C9⋊C16) | 2 |
| C3×#63378 | 2 |
| #10589114 | 3 |
| #10588239 | 3 |