Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
1306 conjugacy classes of subgroups; only the 251 normal subgroups are shown.
This group has 1306 conjugacy classes of subgroups — too many to draw. Only its 251 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. #22624643 | C2 | semidirect |
| 3. #22618637 | C2 | semidirect |
| 4. #22610347 | C2 | semidirect |
| 5. #22610216 | C2 | semidirect |
| 6. #22609734 | C2 | semidirect |
| 7. C73×#1791 | C2 | semidirect |
| 12. C22×#11924011 | C22 | semidirect |
| 18. #17988613 | C22 | semidirect |
| 20. #17988550 | C22 | semidirect |
| 21. #17988545 | C22 | semidirect |
| 22. #17988359 | C22 | semidirect |
| 34. C2×#11924012 | D4 | semidirect |
| 39. C22×#10596831 | D4 | semidirect |
| 150. #1791 | D73 | semidirect |
| 152. C73 | #21484 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22624643 | 2 |
| #22619323 | 2 |
| #22618637 | 2 |
| #22610347 | 2 |
| #22610216 | 2 |
| #22609734 | 2 |
| C73×#1791 | 2 |
| #21484 | 73 |