Finite Group DatabasebetaFinite Group DatabasebetaOrder 17216.
234 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 101 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. #22575448 | C2 | semidirect |
| 2. #22575446 | C2 | semidirect |
| 3. #22575443 | C2 | semidirect |
| 4. #22575439 | C2 | semidirect |
| 5. #22575437 | C2 | semidirect |
| 6. #22575434 | C2 | semidirect |
| 7. #22575430 | C2 | semidirect |
| 9. C4×Dic538 | C2 | semidirect |
| 10. C4×C22⋊D269 | C2 | semidirect |
| 11. C4×C22⋊D269 | C2 | semidirect |
| 12. #22575412 | C2 | semidirect |
| 13. #22575410 | C2 | semidirect |
| 14. C2×C4×Dic269 | C2 | semidirect |
| 15. C4×D4×C269 | C2 | semidirect |
| 103. C269 | #529 | semidirect |
| 116. C4×D4 | D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22575448 | 2 |
| #22575446 | 2 |
| #22575443 | 2 |
| #22575439 | 2 |
| #22575437 | 2 |
| #22575434 | 2 |
| #22575430 | 2 |
| #22575425 | 2 |
| C4×Dic538 | 2 |
| C4×C22⋊D269 | 2 |
| #22575412 | 2 |
| #22575410 | 2 |
| C2×C4×Dic269 | 2 |
| C4×D4×C269 | 2 |
| #529 | 269 |