Finite Group DatabasebetaFinite Group DatabasebetaOrder 17216.
190 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 190 conjugacy classes of subgroups — too many to draw. Only its 55 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×#16864385 | C2 | semidirect |
| 3. #22575411 | C2 | semidirect |
| 4. #22575375 | C2 | semidirect |
| 5. #22575374 | C2 | semidirect |
| 6. #22575373 | C2 | semidirect |
| 7. #102×C269 | C2 | semidirect |
| 12. D4×D269 | C4 | semidirect |
| 15. C2×#14524130 | C22 | semidirect |
| 16. C4⋊Dic269 | C22 | semidirect |
| 20. C2×C8×C269 | C22 | semidirect |
| 21. C4⋊C4×C269 | C22 | semidirect |
| 63. C269 | #418 | semidirect |
| 71. #102 | D269 | semidirect |
| 81. C2×C8 | C2×D269 | semidirect |
| 83. C4⋊C4 | C2×D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×D269 | 2 |
| C2×#16864385 | 2 |
| #22575411 | 2 |
| #22575375 | 2 |
| #22575374 | 2 |
| #22575373 | 2 |
| #102×C269 | 2 |
| #418 | 269 |