Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
320 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 320 conjugacy classes of subgroups — too many to draw. Only its 54 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. #22626229 | C2 | semidirect |
| 2. #22626214 | C2 | semidirect |
| 3. #22625077 | C2 | semidirect |
| 4. #22625076 | C2 | semidirect |
| 5. #22625059 | C2 | semidirect |
| 6. #22625059 | C2 | semidirect |
| 16. #17989193 | C4 | semidirect |
| 19. #17988961 | C4 | semidirect |
| 25. #17988649 | C4 | semidirect |
| 26. #491×C73 | C4 | semidirect |
| 167. C73 | #13606 | semidirect |
| 172. #491 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626229 | 2 |
| #22626214 | 2 |
| #22625077 | 2 |
| #22625076 | 2 |
| #22625059 | 2 |
| #22620993 | 2 |
| #13606 | 73 |