Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
668 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 668 conjugacy classes of subgroups — too many to draw. Only its 135 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. #22623068 | C2 | semidirect |
| 2. #22621730 | C2 | semidirect |
| 3. #22612048 | C2 | semidirect |
| 4. #22612004 | C2 | semidirect |
| 5. #22611887 | C2 | semidirect |
| 6. #22611813 | C2 | semidirect |
| 7. #22611769 | C2 | semidirect |
| 8. C73×#2246 | C2 | semidirect |
| 10. #17989388 | C22 | semidirect |
| 11. #17989023 | C22 | semidirect |
| 16. #17989003 | C22 | semidirect |
| 18. #17988854 | C22 | semidirect |
| 21. #17988705 | C22 | semidirect |
| 22. #17988417 | C22 | semidirect |
| 23. #17988408 | C22 | semidirect |
| 24. #17988400 | C22 | semidirect |
| 25. #17988395 | C22 | semidirect |
| 26. #17988370 | C22 | semidirect |
| 27. C2×D16×C73 | C22 | semidirect |
| 28. C2×D16×C73 | C22 | semidirect |
| 29. #493×C73 | C22 | semidirect |
| 30. C4×C16×C73 | C22 | semidirect |
| 44. Dic584 | D4 | semidirect |
| 45. #14556536 | D4 | semidirect |
| 47. D1168 | D4 | semidirect |
| 145. #2246 | D73 | semidirect |
| 151. C73 | #33858 | semidirect |
| 159. C2×D16 | C2×D73 | semidirect |
| 160. C2×D16 | C2×D73 | semidirect |
| 162. #493 | C2×D73 | semidirect |
| 173. C4×C16 | C2×D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22623068 | 2 |
| #22621730 | 2 |
| #22612048 | 2 |
| #22612004 | 2 |
| #22611887 | 2 |
| #22611813 | 2 |
| #22611769 | 2 |
| C73×#2246 | 2 |
| #33858 | 73 |