Finite Group DatabasebetaFinite Group DatabasebetaOrder 17216.
258 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 147 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. #22575461 | C2 | semidirect |
| 3. #22575459 | C2 | semidirect |
| 4. C2×#16864386 | C2 | semidirect |
| 5. M16×D269 | C2 | semidirect |
| 6. C2×M16×C269 | C2 | semidirect |
| 16. #16864386 | C22 | semidirect |
| 17. #16864385 | C22 | semidirect |
| 18. C2×#14524130 | C22 | semidirect |
| 19. C8×D269 | C22 | semidirect |
| 22. M16×C269 | C22 | semidirect |
| 23. C2×C8×C269 | C22 | semidirect |
| 59. C269 | #568 | semidirect |
| 66. C2×M16 | D269 | semidirect |
| 80. M16 | C2×D269 | semidirect |
| 83. C2×C8 | C2×D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16864402 | 2 |
| #22575461 | 2 |
| #22575459 | 2 |
| C2×#16864386 | 2 |
| M16×D269 | 2 |
| C2×M16×C269 | 2 |
| #568 | 269 |