Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
308 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 112 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 |
|---|---|---|
| 9. #17989512 | C4 | semidirect |
| 10. #17989511 | C4 | semidirect |
| 15. #17988362 | C4 | semidirect |
| 16. #17988362 | C4 | semidirect |
| 17. C4×#11924003 | C4 | semidirect |
| 18. C4×C16×C73 | C4 | semidirect |
| 99. C73 | #12668 | semidirect |
| 111. C4×C16 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626278 | 2 |
| #22625733 | 2 |
| #22625001 | 2 |
| #22624999 | 2 |
| C4×#14556530 | 2 |
| #12668 | 73 |