Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
418 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 93 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. #22558935 | C2 | semidirect |
| 5. #22558079 | C2 | semidirect |
| 6. #22558065 | C2 | semidirect |
| 7. C67×#1988 | C2 | semidirect |
| 9. #16863802 | C4 | semidirect |
| 10. #16863758 | C4 | semidirect |
| 191. #1988 | D67 | semidirect |
| 196. C67 | #9375 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571430 | 2 |
| #22569345 | 2 |
| #22558935 | 2 |
| #22558732 | 2 |
| #22558079 | 2 |
| #22558065 | 2 |
| C67×#1988 | 2 |
| #9375 | 67 |