Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
344 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 96 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 |
|---|---|---|
| 21. #14556646 | C8 | semidirect |
| 122. C73 | #7030 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22625848 | 2 |
| C4×#14556646 | 2 |
| #22609675 | 2 |
| #7030 | 73 |