Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
294 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 294 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. #17989429 | C4 | semidirect |
| 13. #17989429 | C4 | semidirect |
| 14. #17989428 | C4 | semidirect |
| 15. C8×#10596833 | C4 | semidirect |
| 138. C73 | #8141 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22625144 | 2 |
| #22625134 | 2 |
| #22624757 | 2 |
| #22624755 | 2 |
| #22609681 | 2 |
| #8141 | 73 |