Finite Group DatabasebetaFinite Group DatabasebetaOrder 17216.
154 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 48 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. D269⋊M16 | C2 | semidirect |
| 2. #22575532 | C2 | semidirect |
| 3. #22575518 | C2 | semidirect |
| 5. #16864412 | C22 | semidirect |
| 10. C4×#11761640 | C22 | semidirect |
| 13. #16864403 | C4 | semidirect |
| 16. C2×D1076 | C4 | semidirect |
| 19. C2×Q8×C269 | C4 | semidirect |
| 56. C269 | #421 | semidirect |
| 66. C2×Q8 | #11761640 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D269⋊M16 | 2 |
| #22575532 | 2 |
| #22575518 | 2 |
| C2×#16864403 | 2 |
| #421 | 269 |