Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
406 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 91 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. Q8×C3⋊Dic9 | C2 | semidirect |
| 2. C2×C9×#216 | C2 | semidirect |
| 5. #11720298 | C2 | semidirect |
| 7. #11720273 | C2 | semidirect |
| 103. C2×#216 | D9 | semidirect |
| 221. C3×C9 | #464 | semidirect |
| 314. C9 | #5166 | semidirect |
| 353. C3 | #10588865 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×C3⋊Dic9 | 2 |
| C2×C9×#216 | 2 |
| C2×C3×#3675 | 2 |
| #11720951 | 2 |
| #11720298 | 2 |
| #11720283 | 2 |
| #11720273 | 2 |
| #10591612 | 3 |
| #10588865 | 3 |