Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
294 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 96 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. #17989428 | C4 | semidirect |
| 15. C8×#10596833 | C4 | semidirect |
| 19. #17988309 | C4 | semidirect |
| 20. #17988309 | C4 | semidirect |
| 21. #17988308 | C4 | semidirect |
| 22. #322×C73 | C4 | semidirect |
| 124. C73 | #8141 | semidirect |
| 138. #322 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22625649 | 2 |
| #22625135 | 2 |
| #22624756 | 2 |
| #22624754 | 2 |
| #22608222 | 2 |
| #8141 | 73 |