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 |
|---|---|---|
| 9. #17989478 | C4 | semidirect |
| 10. #17989477 | C4 | semidirect |
| 11. #17989476 | C4 | semidirect |
| 12. #17989475 | C4 | semidirect |
| 13. #17989474 | C4 | semidirect |
| 14. #17989473 | C4 | semidirect |
| 15. C4×#11924031 | C4 | semidirect |
| 16. C16×#64408 | C4 | semidirect |
| 22. #17988365 | C4 | semidirect |
| 23. #17988364 | C4 | semidirect |
| 24. #347×C73 | C4 | semidirect |
| 106. C73 | #12542 | semidirect |
| 116. #347 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626151 | 2 |
| #22626143 | 2 |
| #22626141 | 2 |
| #22625653 | 2 |
| #22611534 | 2 |
| #12542 | 73 |