Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
1306 conjugacy classes of subgroups; only the 291 normal subgroups are shown.
This group has 1306 conjugacy classes of subgroups — too many to draw. Only its 291 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 |
| 2. #22618635 | C2 | semidirect |
| 3. #22610350 | C2 | semidirect |
| 4. #22610219 | C2 | semidirect |
| 5. #22609882 | C2 | semidirect |
| 6. #22609733 | C2 | semidirect |
| 12. C22×#11924012 | C22 | semidirect |
| 15. #17988614 | C22 | semidirect |
| 18. #17988551 | C22 | semidirect |
| 19. #17988543 | C22 | semidirect |
| 20. #17988357 | C22 | semidirect |
| 35. C2×#11924012 | D4 | semidirect |
| 39. C22×#10596831 | D4 | 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 |
| #22618635 | 2 |
| #22610350 | 2 |
| #22610219 | 2 |
| #22609882 | 2 |
| #22609733 | 2 |
| C73×#3025 | 2 |
| #21484 | 73 |