Finite Group DatabasebetaFinite Group DatabasebetaOrder 17216.
104 conjugacy classes of subgroups; only the 35 normal subgroups are shown.
This group has 104 conjugacy classes of subgroups — too many to draw. Only its 35 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. #22575484 | C2 | semidirect |
| 3. C2×#16864389 | C2 | semidirect |
| 4. #22575461 | C2 | semidirect |
| 5. #22575388 | C2 | semidirect |
| 6. #22575369 | C2 | semidirect |
| 7. #101×C269 | C2 | semidirect |
| 51. C269 | #471 | semidirect |
| 58. #101 | D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22575484 | 2 |
| #22575481 | 2 |
| C2×#16864389 | 2 |
| #22575461 | 2 |
| #22575388 | 2 |
| #22575369 | 2 |
| #101×C269 | 2 |
| #471 | 269 |