Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
238 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 238 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 |
|---|---|---|
| 25. #14556527 | C8 | semidirect |
| 35. #108×C73 | C8 | semidirect |
| 105. C73 | #7177 | semidirect |
| 128. #108 | #10596833 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989476 | 2 |
| #22625478 | 2 |
| #108×Dic73 | 2 |
| #7177 | 73 |