Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
310 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 108 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. C4×#11924003 | C4 | semidirect |
| 10. C16×Dic73 | C4 | semidirect |
| 11. C4×C16×C73 | C4 | semidirect |
| 72. C73 | #12889 | semidirect |
| 80. C4×C16 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22625868 | 2 |
| #22624989 | 2 |
| C4×C16×D73 | 2 |
| #12889 | 73 |