Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
292 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 292 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 |
|---|---|---|
| 5. C2×#14556686 | C4 | semidirect |
| 7. #17989684 | C4 | semidirect |
| 126. C73 | #7200 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22627099 | 2 |
| #22627096 | 2 |
| #22625669 | 2 |
| #7200 | 73 |