Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
308 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 67 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 |
|---|---|---|
| 3. #22608105 | C2 | semidirect |
| 4. #22608090 | C2 | semidirect |
| 6. #17989199 | C4 | semidirect |
| 8. #17988966 | C4 | semidirect |
| 9. #17988955 | C4 | semidirect |
| 15. #17988648 | C4 | semidirect |
| 148. C73 | #13608 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22621014 | 2 |
| #22611620 | 2 |
| #22608105 | 2 |
| #22608090 | 2 |
| C73×#2129 | 2 |
| #13608 | 73 |