Finite Group DatabasebetaFinite Group DatabasebetaOrder 17216.
270 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 2. C2×Q8×D269 | C2 | semidirect |
| 3. #22575452 | C2 | semidirect |
| 4. #22575439 | C2 | semidirect |
| 5. #22575438 | C2 | semidirect |
| 6. #22575435 | C2 | semidirect |
| 7. #22575433 | C2 | semidirect |
| 8. #22575432 | C2 | semidirect |
| 9. #22575429 | C2 | semidirect |
| 10. #22575411 | C2 | semidirect |
| 11. C22⋊Q8×C269 | C2 | semidirect |
| 83. C269 | #536 | semidirect |
| 94. C22⋊Q8 | D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16864402 | 2 |
| C2×Q8×D269 | 2 |
| #22575452 | 2 |
| #22575439 | 2 |
| #22575438 | 2 |
| #22575435 | 2 |
| #22575433 | 2 |
| #22575432 | 2 |
| #22575429 | 2 |
| #22575411 | 2 |
| C22⋊Q8×C269 | 2 |
| #536 | 269 |