Finite Group DatabasebetaFinite Group DatabasebetaOrder 17216.
268 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 99 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. #22575498 | C2 | semidirect |
| 2. #22575479 | C2 | semidirect |
| 3. #22575477 | C2 | semidirect |
| 4. #22575475 | C2 | semidirect |
| 5. #22575472 | C2 | semidirect |
| 6. D8×D269 | C2 | semidirect |
| 7. #22575459 | C2 | semidirect |
| 8. C2×D8×C269 | C2 | semidirect |
| 10. #16864402 | C22 | semidirect |
| 12. #16864401 | C22 | semidirect |
| 15. D4×D269 | C22 | semidirect |
| 16. Dic1076 | C22 | semidirect |
| 17. #16864391 | C22 | semidirect |
| 18. #16864390 | C22 | semidirect |
| 19. D2152 | C22 | semidirect |
| 20. #16864387 | C22 | semidirect |
| 21. #16864386 | C22 | semidirect |
| 22. #16864385 | C22 | semidirect |
| 23. C8×D269 | C22 | semidirect |
| 24. C2×D4×C269 | C22 | semidirect |
| 25. D8×C269 | C22 | semidirect |
| 26. D8×C269 | C22 | semidirect |
| 27. C2×C8×C269 | C22 | semidirect |
| 62. C269 | #576 | semidirect |
| 70. C2×D8 | D269 | semidirect |
| 79. C2×D4 | C2×D269 | semidirect |
| 85. D8 | C2×D269 | semidirect |
| 86. D8 | C2×D269 | semidirect |
| 90. C2×C8 | C2×D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22575498 | 2 |
| #22575479 | 2 |
| #22575477 | 2 |
| #22575475 | 2 |
| #22575472 | 2 |
| D8×D269 | 2 |
| #22575459 | 2 |
| C2×D8×C269 | 2 |
| #576 | 269 |