Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
396 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 2. #22558972 | C2 | semidirect |
| 3. #22558823 | C2 | semidirect |
| 5. #22558720 | C2 | semidirect |
| 7. C67×#1746 | C2 | semidirect |
| 10. #16863794 | C4 | semidirect |
| 11. #16863769 | C4 | semidirect |
| 12. #16863747 | C4 | semidirect |
| 13. #16863743 | C4 | semidirect |
| 178. #1746 | D67 | semidirect |
| 184. C67 | #9766 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570768 | 2 |
| #22558972 | 2 |
| #22558823 | 2 |
| #22558819 | 2 |
| #22558720 | 2 |
| #22558716 | 2 |
| C67×#1746 | 2 |
| #9766 | 67 |