Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
566 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 566 conjugacy classes of subgroups — too many to draw. Only its 106 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 |
|---|---|---|
| 13. #17988483 | C4 | semidirect |
| 14. #17988483 | C4 | semidirect |
| 19. #17988453 | C4 | semidirect |
| 22. C2×#125×C73 | C4 | semidirect |
| 195. C73 | #9886 | semidirect |
| 196. C2×#125 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14556648 | 2 |
| #22625107 | 2 |
| #22624804 | 2 |
| #22618236 | 2 |
| #9886 | 73 |