Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
502 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 502 conjugacy classes of subgroups — too many to draw. Only its 89 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×#63498 | C2 | semidirect |
| 3. #11720887 | C2 | semidirect |
| 4. #11720575 | C2 | semidirect |
| 5. #11720301 | C2 | semidirect |
| 13. C2×C3×Dic18 | C22 | semidirect |
| 14. #88532 | C22 | semidirect |
| 16. C3×C4×Dic9 | C22 | semidirect |
| 26. #63498 | D3 | semidirect |
| 63. C2×Dic18 | C2×D3 | semidirect |
| 67. C4×Dic9 | C2×D3 | semidirect |
| 178. C3×C9 | #455 | semidirect |
| 257. C9 | #5061 | semidirect |
| 293. C3 | #10588921 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#1004 | 2 |
| C3×#63498 | 2 |
| #11720887 | 2 |
| #11720575 | 2 |
| #11720301 | 2 |
| #10591512 | 3 |
| #10588921 | 3 |