Finite Group DatabasebetaFinite Group DatabasebetaOrder 17216.
228 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 228 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. #22575452 | C2 | semidirect |
| 2. #22575443 | C2 | semidirect |
| 3. #22575433 | C2 | semidirect |
| 4. #22575430 | C2 | semidirect |
| 5. #22575429 | C2 | semidirect |
| 6. Q8×Dic269 | C2 | semidirect |
| 9. C2×C4⋊Dic269 | C2 | semidirect |
| 10. C4⋊C4×D269 | C2 | semidirect |
| 11. C22⋊Q8×C269 | C2 | semidirect |
| 37. C22⋊D269 | Q8 | semidirect |
| 74. C269 | #554 | semidirect |
| 81. C22⋊Q8 | D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22575452 | 2 |
| #22575443 | 2 |
| #22575433 | 2 |
| #22575430 | 2 |
| #22575429 | 2 |
| Q8×Dic269 | 2 |
| C4×C22⋊D269 | 2 |
| #22575413 | 2 |
| C2×C4⋊Dic269 | 2 |
| C4⋊C4×D269 | 2 |
| C22⋊Q8×C269 | 2 |
| #554 | 269 |