Finite Group DatabasebetaFinite Group DatabasebetaOrder 17728.
216 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 93 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. #22579878 | C2 | semidirect |
| 2. #22579875 | C2 | semidirect |
| 3. #22579873 | C2 | semidirect |
| 4. #22579869 | C2 | semidirect |
| 5. #22579866 | C2 | semidirect |
| 6. #22579866 | C2 | semidirect |
| 7. #22579865 | C2 | semidirect |
| 8. #22579863 | C2 | semidirect |
| 9. #22579858 | C2 | semidirect |
| 10. #22579858 | C2 | semidirect |
| 12. #22579845 | C2 | semidirect |
| 13. C4×C22⋊D277 | C2 | semidirect |
| 14. #22579838 | C2 | semidirect |
| 15. C22⋊Q8×C277 | C2 | semidirect |
| 103. C277 | #542 | semidirect |
| 115. C22⋊Q8 | D277 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22579878 | 2 |
| #22579875 | 2 |
| #22579873 | 2 |
| #22579869 | 2 |
| #22579866 | 2 |
| #22579865 | 2 |
| #22579863 | 2 |
| #22579858 | 2 |
| #22579853 | 2 |
| #22579845 | 2 |
| C4×C22⋊D277 | 2 |
| #22579838 | 2 |
| C22⋊Q8×C277 | 2 |
| #542 | 277 |