Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
516 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 98 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 |
|---|---|---|
| 3. #22624750 | C2 | semidirect |
| 4. #22624750 | C2 | semidirect |
| 190. C73 | #7613 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22625787 | 2 |
| #22625657 | 2 |
| #22624750 | 2 |
| #22612413 | 2 |
| #7613 | 73 |