Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
308 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 77 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×Dic36 | C2 | semidirect |
| 3. C9×#812 | C2 | semidirect |
| 4. #11720235 | C2 | semidirect |
| 5. #11720234 | C2 | semidirect |
| 24. C2×Dic36 | D3 | semidirect |
| 77. #812 | D9 | semidirect |
| 156. C3×C9 | #510 | semidirect |
| 221. C9 | #5179 | semidirect |
| 248. C3 | #10588589 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11721773 | 2 |
| C2×C3×Dic36 | 2 |
| C9×#812 | 2 |
| #11720235 | 2 |
| #11720234 | 2 |
| #10590642 | 3 |
| #10588589 | 3 |