Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
254 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 254 conjugacy classes of subgroups — too many to draw. Only its 77 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 |
|---|---|---|
| 7. #17989690 | C4 | semidirect |
| 9. C4×#11924040 | C4 | semidirect |
| 111. C73 | #7168 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22627121 | 2 |
| C4×#14556688 | 2 |
| #22625728 | 2 |
| #7168 | 73 |