Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
528 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 89 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. #22627099 | C2 | semidirect |
| 2. #22627096 | C2 | semidirect |
| 3. #22626955 | C2 | semidirect |
| 7. #17989684 | C22 | semidirect |
| 8. #17989684 | C22 | semidirect |
| 168. C73 | #11422 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22627099 | 2 |
| #22627096 | 2 |
| #22626955 | 2 |
| C2×#17989562 | 2 |
| #11422 | 73 |