Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
262 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 6. #17989690 | C4 | semidirect |
| 9. #17989681 | C4 | semidirect |
| 111. C73 | #7170 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22627117 | 2 |
| #22627087 | 2 |
| #22625728 | 2 |
| #7170 | 73 |