Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
520 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 123 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. #22620674 | C2 | semidirect |
| 3. #22612149 | C2 | semidirect |
| 4. #22612103 | C2 | semidirect |
| 5. #22612102 | C2 | semidirect |
| 6. #22612009 | C2 | semidirect |
| 8. #22611825 | C2 | semidirect |
| 9. #22611823 | C2 | semidirect |
| 10. #22611742 | C2 | semidirect |
| 11. C73×#2214 | C2 | semidirect |
| 16. #17988985 | C22 | semidirect |
| 26. #17988694 | C22 | semidirect |
| 30. #17988411 | C22 | semidirect |
| 31. #17988410 | C22 | semidirect |
| 32. #17988408 | C22 | semidirect |
| 33. #17988403 | C22 | semidirect |
| 37. #17988364 | C22 | semidirect |
| 39. #494×C73 | C22 | semidirect |
| 41. #364×C73 | C22 | semidirect |
| 42. #362×C73 | C22 | semidirect |
| 219. #2214 | D73 | semidirect |
| 224. C73 | #33689 | semidirect |
| 231. #494 | C2×D73 | semidirect |
| 249. #364 | C2×D73 | semidirect |
| 251. #362 | C2×D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620674 | 2 |
| #22618836 | 2 |
| #22612149 | 2 |
| #22612103 | 2 |
| #22612102 | 2 |
| #22612009 | 2 |
| #22611880 | 2 |
| #22611825 | 2 |
| #22611823 | 2 |
| #22611742 | 2 |
| C73×#2214 | 2 |
| #33689 | 73 |