Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
370 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 108 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. #17988991 | C4 | semidirect |
| 13. #17988989 | C4 | semidirect |
| 19. #499×C73 | C4 | semidirect |
| 23. #14556666 | Q8 | semidirect |
| 113. C73 | #13287 | semidirect |
| 119. #499 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626138 | 2 |
| #22625866 | 2 |
| #22625002 | 2 |
| #22620444 | 2 |
| #13287 | 73 |