Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
672 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 672 conjugacy classes of subgroups — too many to draw. Only its 99 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. #22611605 | C2 | semidirect |
| 4. #22611586 | C2 | semidirect |
| 5. #22608061 | C2 | semidirect |
| 6. #22608051 | C2 | semidirect |
| 8. C2×#14556621 | C4 | semidirect |
| 9. C22×#11924016 | C4 | semidirect |
| 16. #17988592 | C4 | semidirect |
| 17. #17988583 | C4 | semidirect |
| 31. C22×Dic146 | C2×C4 | semidirect |
| 38. C2×#11924012 | C2×C4 | semidirect |
| 39. C22×#10596831 | C2×C4 | semidirect |
| 50. #14556550 | C2×C4 | semidirect |
| 259. C73 | #13100 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22619208 | 2 |
| #22618392 | 2 |
| #22611605 | 2 |
| #22611586 | 2 |
| #22608061 | 2 |
| #22608051 | 2 |
| C73×#1795 | 2 |
| #13100 | 73 |