Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
302 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 302 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 |
|---|---|---|
| 13. #17988363 | C4 | semidirect |
| 14. C16×Dic73 | C4 | semidirect |
| 15. #346×C73 | C4 | semidirect |
| 94. C73 | #12886 | semidirect |
| 104. #346 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22625871 | 2 |
| #22625866 | 2 |
| #22624996 | 2 |
| #22611524 | 2 |
| #12886 | 73 |