Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
422 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 422 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. #22558720 | C2 | semidirect |
| 5. #22558683 | C2 | semidirect |
| 6. #22558071 | C2 | semidirect |
| 7. C67×#1274 | C2 | semidirect |
| 10. #16863801 | C4 | semidirect |
| 11. #16863794 | C4 | semidirect |
| 12. #16863743 | C4 | semidirect |
| 13. #16863743 | C4 | semidirect |
| 175. #1274 | D67 | semidirect |
| 176. C67 | #9279 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571347 | 2 |
| #22569284 | 2 |
| #22558720 | 2 |
| #22558716 | 2 |
| #22558683 | 2 |
| #22558071 | 2 |
| C67×#1274 | 2 |
| #9279 | 67 |