Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
370 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 89 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×#870 | C2 | semidirect |
| 3. #11720516 | C2 | semidirect |
| 4. #11720266 | C2 | semidirect |
| 54. #870 | D9 | semidirect |
| 114. C3×C9 | #490 | semidirect |
| 163. C9 | #5071 | semidirect |
| 186. C3 | #10588748 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#63436 | 2 |
| C9×#870 | 2 |
| #11720516 | 2 |
| #11720266 | 2 |
| #10590279 | 3 |
| #10588748 | 3 |