Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
354 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 104 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 |
|---|---|---|
| 12. #17988992 | C4 | semidirect |
| 14. #17988988 | C4 | semidirect |
| 19. #500×C73 | C4 | semidirect |
| 22. #14556666 | Q8 | semidirect |
| 128. C73 | #13288 | semidirect |
| 132. #500 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626138 | 2 |
| #22625868 | 2 |
| #22625002 | 2 |
| #22620442 | 2 |
| #13288 | 73 |