Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
1004 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 1004 conjugacy classes of subgroups — too many to draw. Only its 179 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. #22620869 | C2 | semidirect |
| 3. #22609009 | C2 | semidirect |
| 4. #22608990 | C2 | semidirect |
| 5. #22608593 | C2 | semidirect |
| 6. #22608352 | C2 | semidirect |
| 7. C73×#3550 | C2 | semidirect |
| 19. #17988336 | C22 | semidirect |
| 20. #17988331 | C22 | semidirect |
| 21. Q8⋊#10596831 | C22 | semidirect |
| 23. #559×C73 | C22 | semidirect |
| 24. Q82×C73 | C22 | semidirect |
| 168. #3550 | D73 | semidirect |
| 175. C73 | #18718 | semidirect |
| 178. #559 | C2×D73 | semidirect |
| 179. Q82 | C2×D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620869 | 2 |
| #22620384 | 2 |
| #22609009 | 2 |
| #22608990 | 2 |
| #22608593 | 2 |
| #22608352 | 2 |
| C73×#3550 | 2 |
| #18718 | 73 |