Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
716 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 716 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 4. #22560145 | C2 | semidirect |
| 5. #22560143 | C2 | semidirect |
| 6. #22558076 | C2 | semidirect |
| 7. C67×#1289 | C2 | semidirect |
| 19. #16863317 | C4 | semidirect |
| 20. #16863309 | C4 | semidirect |
| 249. #1289 | D67 | semidirect |
| 250. C67 | #9471 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22569235 | 2 |
| #22563575 | 2 |
| #22560194 | 2 |
| #22560145 | 2 |
| #22560143 | 2 |
| #22558076 | 2 |
| C67×#1289 | 2 |
| #9471 | 67 |