Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
1380 conjugacy classes of subgroups; only the 211 normal subgroups are shown.
This group has 1380 conjugacy classes of subgroups — too many to draw. Only its 211 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×#17989023 | C2 | semidirect |
| 2. #22619512 | C2 | semidirect |
| 3. #22611860 | C2 | semidirect |
| 4. #22611843 | C2 | semidirect |
| 5. #22611647 | C2 | semidirect |
| 6. #22611542 | C2 | semidirect |
| 7. C23×D8×C73 | C2 | semidirect |
| 8. C2×#14556613 | C22 | semidirect |
| 11. C2×#14556535 | C22 | semidirect |
| 12. C2×#14556532 | C22 | semidirect |
| 13. C2×#14556531 | C22 | semidirect |
| 14. #17988828 | C22 | semidirect |
| 15. #17988823 | C22 | semidirect |
| 17. #17988625 | C22 | semidirect |
| 19. #17988388 | C22 | semidirect |
| 20. C22⋊#11924003 | C22 | semidirect |
| 30. C2×Dic292 | C23 | semidirect |
| 32. C2×D584 | C23 | semidirect |
| 42. C2×#11924003 | C23 | semidirect |
| 43. #14556525 | C23 | semidirect |
| 61. C2×D8×C73 | D4 | semidirect |
| 162. C22×C73 | #509 | semidirect |
| 179. C23×D8 | D73 | semidirect |
| 186. C73 | #33517 | semidirect |
| 226. C2×D8 | C22⋊D73 | semidirect |
| 343. C22 | #17989023 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989023 | 2 |
| #22619512 | 2 |
| #22611860 | 2 |
| #22611843 | 2 |
| #22611647 | 2 |
| #22611542 | 2 |
| C23×D8×C73 | 2 |
| #33517 | 73 |