Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
324 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 81 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 |
|---|---|---|
| 3. #11720540 | C2 | semidirect |
| 5. C9×#816 | C2 | semidirect |
| 6. #11720298 | C2 | semidirect |
| 7. #11720262 | C2 | semidirect |
| 100. #816 | D9 | semidirect |
| 196. C3×C9 | #485 | semidirect |
| 278. C9 | #4723 | semidirect |
| 315. C3 | #10588495 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11720944 | 2 |
| #11720907 | 2 |
| #11720540 | 2 |
| C3×(C2×D9)⋊C8 | 2 |
| C9×#816 | 2 |
| #11720298 | 2 |
| #11720262 | 2 |
| #10590711 | 3 |
| #10588495 | 3 |