Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
468 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 468 conjugacy classes of subgroups — too many to draw. Only its 88 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 |
|---|---|---|
| 14. #17988518 | C4 | semidirect |
| 18. #17988453 | C4 | semidirect |
| 19. C2×C4⋊Q8×C73 | C4 | semidirect |
| 161. C73 | #11694 | semidirect |
| 162. C2×C4⋊Q8 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22625630 | 2 |
| #22625164 | 2 |
| #22624911 | 2 |
| #22615698 | 2 |
| #11694 | 73 |