Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
1380 conjugacy classes of subgroups; only the 195 normal subgroups are shown.
This group has 1380 conjugacy classes of subgroups — too many to draw. Only its 195 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. C23×D584 | C2 | semidirect |
| 2. C2×#17989025 | C2 | semidirect |
| 3. #22619512 | C2 | semidirect |
| 4. #22611862 | C2 | semidirect |
| 5. #22611845 | C2 | semidirect |
| 6. #22611648 | C2 | semidirect |
| 7. C73×#2112 | C2 | semidirect |
| 9. C2×#14556613 | C22 | semidirect |
| 17. C2×#14556536 | C22 | semidirect |
| 18. C2×D1168 | C22 | semidirect |
| 19. #17988828 | C22 | semidirect |
| 20. #17988823 | C22 | semidirect |
| 22. #17988625 | C22 | semidirect |
| 24. #17988389 | C22 | semidirect |
| 26. C2×M32×C73 | C22 | semidirect |
| 27. C22⋊C16×C73 | C22 | semidirect |
| 37. C2×Dic292 | C23 | semidirect |
| 45. C2×D584 | D4 | semidirect |
| 47. C2×D584 | C23 | semidirect |
| 56. #14556525 | C23 | semidirect |
| 67. C2×C16×C73 | C23 | semidirect |
| 158. C22×C73 | #509 | semidirect |
| 185. #2112 | D73 | semidirect |
| 186. C73 | #33517 | semidirect |
| 199. C2×M32 | C2×D73 | semidirect |
| 206. C22⋊C16 | C2×D73 | semidirect |
| 242. C2×C16 | C22×D73 | semidirect |
| 343. C22 | #17989025 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D584 | 2 |
| C2×#17989025 | 2 |
| #22619512 | 2 |
| #22611862 | 2 |
| #22611845 | 2 |
| #22611648 | 2 |
| C73×#2112 | 2 |
| #33517 | 73 |