Finite Group DatabasebetaFinite Group DatabasebetaOrder 17216.
258 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 107 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. #22575500 | C2 | semidirect |
| 2. #22575483 | C2 | semidirect |
| 3. #22575479 | C2 | semidirect |
| 4. #22575473 | C2 | semidirect |
| 5. C2×#16864390 | C2 | semidirect |
| 6. #22575460 | C2 | semidirect |
| 7. H(5,𝔽2)×C269 | C2 | semidirect |
| 8. #16864402 | C22 | semidirect |
| 10. C2×Dic538 | C22 | semidirect |
| 12. #16864392 | C22 | semidirect |
| 13. #16864390 | C22 | semidirect |
| 14. #16864390 | C22 | semidirect |
| 15. #16864389 | C22 | semidirect |
| 16. #16864387 | C22 | semidirect |
| 17. #16864386 | C22 | semidirect |
| 18. C2×#14524130 | C22 | semidirect |
| 53. C269 | #577 | semidirect |
| 56. H(5,𝔽2) | D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22575500 | 2 |
| #22575483 | 2 |
| #22575479 | 2 |
| #22575473 | 2 |
| C2×#16864390 | 2 |
| #22575460 | 2 |
| H(5,𝔽2)×C269 | 2 |
| #577 | 269 |