Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
414 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 414 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 |
|---|---|---|
| 3. #22561191 | C2 | semidirect |
| 5. #22558101 | C2 | semidirect |
| 6. #22558100 | C2 | semidirect |
| 7. C67×#1497 | C2 | semidirect |
| 9. #16863802 | C4 | semidirect |
| 10. #16863788 | C4 | semidirect |
| 11. #16863764 | C4 | semidirect |
| 12. #16863758 | C4 | semidirect |
| 203. #1497 | D67 | semidirect |
| 206. C67 | #8998 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570809 | 2 |
| #22569381 | 2 |
| #22561191 | 2 |
| #22558696 | 2 |
| #22558101 | 2 |
| #22558100 | 2 |
| C67×#1497 | 2 |
| #8998 | 67 |