Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
246 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 246 conjugacy classes of subgroups — too many to draw. Only its 112 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 |
|---|---|---|
| 16. #14556665 | C8 | semidirect |
| 20. C2×#11924031 | C8 | semidirect |
| 94. C73 | #7140 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14556665 | 2 |
| C2×#17989475 | 2 |
| #22608215 | 2 |
| #7140 | 73 |