Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
778 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 778 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. #22621743 | C2 | semidirect |
| 2. #22621530 | C2 | semidirect |
| 3. #22609393 | C2 | semidirect |
| 4. #22609365 | C2 | semidirect |
| 5. #22609163 | C2 | semidirect |
| 6. #22608983 | C2 | semidirect |
| 7. #22608817 | C2 | semidirect |
| 8. C8×D584 | C2 | semidirect |
| 9. C73×#1706 | C2 | semidirect |
| 12. #17989222 | C22 | semidirect |
| 14. #17988864 | C22 | semidirect |
| 17. #17988789 | C22 | semidirect |
| 25. #17988666 | C22 | semidirect |
| 26. C8×D292 | C22 | semidirect |
| 28. #17988340 | C22 | semidirect |
| 29. #17988340 | C22 | semidirect |
| 30. #17988333 | C22 | semidirect |
| 31. #17988331 | C22 | semidirect |
| 32. #17988316 | C22 | semidirect |
| 33. #17988316 | C22 | semidirect |
| 34. #500×C73 | C22 | semidirect |
| 36. #492×C73 | C22 | semidirect |
| 37. #486×C73 | C22 | semidirect |
| 38. C82×C73 | C22 | semidirect |
| 100. D584 | D8 | semidirect |
| 195. #1706 | D73 | semidirect |
| 202. C73 | #19884 | semidirect |
| 206. #500 | C2×D73 | semidirect |
| 208. #492 | C2×D73 | semidirect |
| 209. #486 | C2×D73 | semidirect |
| 231. C82 | C2×D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22621743 | 2 |
| #22621530 | 2 |
| #22609393 | 2 |
| #22609365 | 2 |
| #22609163 | 2 |
| #22608983 | 2 |
| #22608817 | 2 |
| C8×D584 | 2 |
| C73×#1706 | 2 |
| #19884 | 73 |