Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
262 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 63 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. C3×#63372 | C2 | semidirect |
| 3. C9×#812 | C2 | semidirect |
| 18. #63372 | D3 | semidirect |
| 55. #812 | D9 | semidirect |
| 114. C3×C9 | #361 | semidirect |
| 167. C9 | #4495 | semidirect |
| 190. C3 | #10588193 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88525 | 2 |
| C3×#63372 | 2 |
| C9×#812 | 2 |
| #10589128 | 3 |
| #10588193 | 3 |