Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
424 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 424 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 |
|---|---|---|
| 2. #22569194 | C2 | semidirect |
| 3. #22558784 | C2 | semidirect |
| 4. #22558755 | C2 | semidirect |
| 5. #22558627 | C2 | semidirect |
| 6. #22558070 | C2 | semidirect |
| 7. C67×#1288 | C2 | semidirect |
| 10. #16863790 | C4 | semidirect |
| 11. #16863785 | C4 | semidirect |
| 12. #16863765 | C4 | semidirect |
| 13. #16863761 | C4 | semidirect |
| 210. #1288 | D67 | semidirect |
| 212. C67 | #9370 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571248 | 2 |
| #22569194 | 2 |
| #22558784 | 2 |
| #22558755 | 2 |
| #22558627 | 2 |
| #22558070 | 2 |
| C67×#1288 | 2 |
| #9370 | 67 |