Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
760 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 760 conjugacy classes of subgroups — too many to draw. Only its 171 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. #11721866 | C2 | semidirect |
| 3. #11721836 | C2 | semidirect |
| 4. #11720585 | C2 | semidirect |
| 5. #11720575 | C2 | semidirect |
| 13. C2×#6226 | C22 | semidirect |
| 17. C4×C3⋊Dic9 | C22 | semidirect |
| 18. #88532 | C22 | semidirect |
| 164. C3×C9 | #455 | semidirect |
| 231. C9 | #5242 | semidirect |
| 263. C3 | #10588921 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C9×H(5,𝔽2) | 2 |
| #11721866 | 2 |
| #11721836 | 2 |
| #11720585 | 2 |
| #11720575 | 2 |
| #10592941 | 3 |
| #10588921 | 3 |