Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
322 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 65 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 |
|---|---|---|
| 17. C22×#10596833 | C8 | semidirect |
| 25. C2×#11924012 | C8 | semidirect |
| 30. C2×M16×C73 | C8 | semidirect |
| 125. C73 | #7188 | semidirect |
| 138. C2×M16 | #10596842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22627043 | 2 |
| #22625599 | 2 |
| #7188 | 73 |