Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
668 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 668 conjugacy classes of subgroups — too many to draw. Only its 143 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. #22623069 | C2 | semidirect |
| 2. #22621731 | C2 | semidirect |
| 3. #22612181 | C2 | semidirect |
| 4. #22612052 | C2 | semidirect |
| 5. #22612007 | C2 | semidirect |
| 6. #22611889 | C2 | semidirect |
| 7. #22611769 | C2 | semidirect |
| 8. C73×#2178 | C2 | semidirect |
| 10. #17989389 | C22 | semidirect |
| 12. #17989022 | C22 | semidirect |
| 14. C2×D1168 | C22 | semidirect |
| 15. C2×D1168 | C22 | semidirect |
| 17. #17989003 | C22 | semidirect |
| 18. #17988964 | C22 | semidirect |
| 19. #17988858 | C22 | semidirect |
| 23. #17988408 | C22 | semidirect |
| 24. #17988399 | C22 | semidirect |
| 25. #17988370 | C22 | semidirect |
| 27. #443×C73 | C22 | semidirect |
| 28. #368×C73 | C22 | semidirect |
| 29. #359×C73 | C22 | semidirect |
| 30. C4×C16×C73 | C22 | semidirect |
| 58. Q32×C73 | D4 | semidirect |
| 59. SD32×C73 | D4 | semidirect |
| 60. D16×C73 | D4 | semidirect |
| 149. #2178 | D73 | semidirect |
| 151. C73 | #33858 | semidirect |
| 167. #443 | C2×D73 | semidirect |
| 168. #368 | C2×D73 | semidirect |
| 171. #359 | C2×D73 | semidirect |
| 173. C4×C16 | C2×D73 | semidirect |
| 190. Q32 | D292 | semidirect |
| 192. SD32 | D292 | semidirect |
| 197. D16 | D292 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22623069 | 2 |
| #22621731 | 2 |
| #22612181 | 2 |
| #22612052 | 2 |
| #22612007 | 2 |
| #22611889 | 2 |
| #22611769 | 2 |
| C73×#2178 | 2 |
| #33858 | 73 |