Finite Group DatabasebetaFinite Group DatabasebetaOrder 17216.
120 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 39 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. C2×#16864390 | C2 | semidirect |
| 2. C2×#16864385 | C2 | semidirect |
| 3. #22575433 | C2 | semidirect |
| 5. #22575386 | C2 | semidirect |
| 6. #22575378 | C2 | semidirect |
| 7. #102×C269 | C2 | semidirect |
| 30. #14524130 | D4 | semidirect |
| 55. C269 | #468 | semidirect |
| 63. #102 | D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16864390 | 2 |
| C2×#16864385 | 2 |
| #22575433 | 2 |
| #22575424 | 2 |
| #22575386 | 2 |
| #22575378 | 2 |
| #102×C269 | 2 |
| #468 | 269 |