Finite Group DatabasebetaFinite Group DatabasebetaOrder 17216.
162 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 43 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×#16864403 | C2 | semidirect |
| 2. C2×#16864387 | C2 | semidirect |
| 3. #22575424 | C2 | semidirect |
| 4. #22575377 | C2 | semidirect |
| 5. #22575375 | C2 | semidirect |
| 6. #22575365 | C2 | semidirect |
| 7. C2×SD16×C269 | C2 | semidirect |
| 27. D1076 | D4 | semidirect |
| 37. Q8×C269 | D4 | semidirect |
| 64. C269 | #449 | semidirect |
| 67. C2×SD16 | D269 | semidirect |
| 92. Q8 | C22⋊D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16864403 | 2 |
| C2×#16864387 | 2 |
| #22575424 | 2 |
| #22575377 | 2 |
| #22575375 | 2 |
| #22575365 | 2 |
| C2×SD16×C269 | 2 |
| #449 | 269 |