Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
350 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 105 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×C9×#97 | C2 | semidirect |
| 3. #11720516 | C2 | semidirect |
| 17. C9×#97 | D3 | semidirect |
| 54. C3×#97 | D9 | semidirect |
| 113. #97 | C3⋊D9 | semidirect |
| 114. C3×C9 | #329 | semidirect |
| 165. C9 | #4464 | semidirect |
| 191. C3 | #10588142 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11721712 | 2 |
| C3×C9×#97 | 2 |
| #11720516 | 2 |
| #10589330 | 3 |
| #10588142 | 3 |