Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
1326 conjugacy classes of subgroups; only the 352 normal subgroups are shown.
This group has 1326 conjugacy classes of subgroups — too many to draw. Only its 352 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 |
|---|---|---|
| 7. #17989533 | C4 | semidirect |
| 8. #17989532 | C4 | semidirect |
| 12. #17988455 | C4 | semidirect |
| 13. #17988454 | C4 | semidirect |
| 15. #383×C73 | C4 | semidirect |
| 50. C4×Dic73 | C42 | semidirect |
| 53. C42×C73 | C42 | semidirect |
| 99. C73 | #13830 | semidirect |
| 107. #383 | #64408 | semidirect |
| 148. C42 | C4×#64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989533 | 2 |
| C2×#17989532 | 2 |
| #22625111 | 2 |
| #383×D73 | 2 |
| #13830 | 73 |