Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
292 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 123 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. #17988416 | C4 | semidirect |
| 15. #17988409 | C4 | semidirect |
| 16. #17988364 | C4 | semidirect |
| 116. C73 | #12678 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22611725 | 2 |
| #22611703 | 2 |
| C2×#17988364 | 2 |
| #22609839 | 2 |
| #22609817 | 2 |
| #22608043 | 2 |
| C73×#1389 | 2 |
| #12678 | 73 |