Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
420 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 85 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. #22558846 | C2 | semidirect |
| 4. #22558759 | C2 | semidirect |
| 6. #22558081 | C2 | semidirect |
| 7. C67×#1288 | C2 | semidirect |
| 10. #16863801 | C4 | semidirect |
| 11. #16863769 | C4 | semidirect |
| 12. #16863747 | C4 | semidirect |
| 13. #16863743 | C4 | semidirect |
| 166. #1288 | D67 | semidirect |
| 167. C67 | #9415 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570927 | 2 |
| #22569279 | 2 |
| #22558846 | 2 |
| #22558759 | 2 |
| #22558755 | 2 |
| #22558081 | 2 |
| C67×#1288 | 2 |
| #9415 | 67 |