Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
396 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 95 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 |
|---|---|---|
| 1. C2×#88547 | C2 | semidirect |
| 2. Q8×C9×Dic3 | C2 | semidirect |
| 5. #11720269 | C2 | semidirect |
| 7. Dic3⋊(C9⋊C8) | C2 | semidirect |
| 98. Q8×Dic3 | D9 | semidirect |
| 218. C3×C9 | #464 | semidirect |
| 310. C9 | #5166 | semidirect |
| 349. C3 | #10588711 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88547 | 2 |
| Q8×C9×Dic3 | 2 |
| C2×C3×#3675 | 2 |
| #11720948 | 2 |
| #11720269 | 2 |
| #11720266 | 2 |
| Dic3⋊(C9⋊C8) | 2 |
| #10591604 | 3 |
| #10588711 | 3 |