Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
408 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 60 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. #22626224 | C2 | semidirect |
| 2. #22626204 | C2 | semidirect |
| 3. #22625060 | C2 | semidirect |
| 4. #22625058 | C2 | semidirect |
| 16. #17988979 | C4 | semidirect |
| 19. #17988974 | C4 | semidirect |
| 21. C2×#14556502 | C4 | semidirect |
| 22. #532×C73 | C4 | semidirect |
| 178. C73 | #13577 | semidirect |
| 182. #532 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626224 | 2 |
| #22626204 | 2 |
| #22625060 | 2 |
| #22625058 | 2 |
| #22620376 | 2 |
| #13577 | 73 |