Finite Group DatabasebetaFinite Group DatabasebetaOrder 17216.
216 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 216 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 |
|---|---|---|
| 1. #22575451 | C2 | semidirect |
| 2. #22575448 | C2 | semidirect |
| 3. #22575446 | C2 | semidirect |
| 4. #22575442 | C2 | semidirect |
| 5. #22575439 | C2 | semidirect |
| 6. #22575439 | C2 | semidirect |
| 7. #22575438 | C2 | semidirect |
| 8. #22575436 | C2 | semidirect |
| 9. #22575431 | C2 | semidirect |
| 10. #22575431 | C2 | semidirect |
| 12. #22575418 | C2 | semidirect |
| 13. C4×C22⋊D269 | C2 | semidirect |
| 14. #22575411 | C2 | semidirect |
| 15. C22⋊Q8×C269 | C2 | semidirect |
| 103. C269 | #542 | semidirect |
| 115. C22⋊Q8 | D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22575451 | 2 |
| #22575448 | 2 |
| #22575446 | 2 |
| #22575442 | 2 |
| #22575439 | 2 |
| #22575438 | 2 |
| #22575436 | 2 |
| #22575431 | 2 |
| #22575426 | 2 |
| #22575418 | 2 |
| C4×C22⋊D269 | 2 |
| #22575411 | 2 |
| C22⋊Q8×C269 | 2 |
| #542 | 269 |