Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
414 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 92 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 |
|---|---|---|
| 1. #22625856 | C2 | semidirect |
| 2. #22625476 | C2 | semidirect |
| 4. #22624800 | C2 | semidirect |
| 172. C73 | #8688 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22625856 | 2 |
| #22625476 | 2 |
| #22625442 | 2 |
| #22624800 | 2 |
| #22618640 | 2 |
| #8688 | 73 |