Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
350 conjugacy classes of subgroups; only the 160 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 160 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 |
|---|---|---|
| 8. #17989480 | C4 | semidirect |
| 9. #17989479 | C4 | semidirect |
| 10. #17989478 | C4 | semidirect |
| 11. #17989477 | C4 | semidirect |
| 12. #17989474 | C4 | semidirect |
| 13. C16×#64408 | C4 | semidirect |
| 20. #17988362 | C4 | semidirect |
| 21. C4×#11924003 | C4 | semidirect |
| 22. C16×Dic73 | C4 | semidirect |
| 23. #346×C73 | C4 | semidirect |
| 103. C73 | #12542 | semidirect |
| 115. #346 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626153 | 2 |
| #22626150 | 2 |
| #22626139 | 2 |
| #22625652 | 2 |
| #22611529 | 2 |
| #12542 | 73 |