Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
366 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 366 conjugacy classes of subgroups — too many to draw. Only its 92 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 |
|---|---|---|
| 14. #17988985 | C4 | semidirect |
| 16. #17988984 | C4 | semidirect |
| 21. #498×C73 | C4 | semidirect |
| 28. #14556661 | Q8 | semidirect |
| 29. #14556660 | Q8 | semidirect |
| 138. C73 | #13272 | semidirect |
| 145. #498 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626270 | 2 |
| #22625733 | 2 |
| #22625004 | 2 |
| #22624995 | 2 |
| #498×D73 | 2 |
| #13272 | 73 |