Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
906 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 906 conjugacy classes of subgroups — too many to draw. Only its 179 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 |
|---|---|---|
| 1. #22570787 | C2 | semidirect |
| 2. #22570786 | C2 | semidirect |
| 3. #22570636 | C2 | semidirect |
| 4. #22570632 | C2 | semidirect |
| 5. #22559882 | C2 | semidirect |
| 6. #22559880 | C2 | semidirect |
| 7. #22559878 | C2 | semidirect |
| 8. #22559876 | C2 | semidirect |
| 9. #22559874 | C2 | semidirect |
| 10. #322×D67 | C2 | semidirect |
| 11. C67×#1721 | C2 | semidirect |
| 113. C8×D67 | D8 | semidirect |
| 202. #1721 | D67 | semidirect |
| 204. C67 | #19616 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570787 | 2 |
| #22570786 | 2 |
| #22570636 | 2 |
| #22570632 | 2 |
| #22559882 | 2 |
| #22559880 | 2 |
| #22559878 | 2 |
| #22559876 | 2 |
| #22559874 | 2 |
| #322×D67 | 2 |
| C67×#1721 | 2 |
| #19616 | 67 |