Finite Group DatabasebetaFinite Group DatabasebetaOrder 17216.
258 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 111 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. C22×Dic538 | C2 | semidirect |
| 3. #22575486 | C2 | direct (N × H) |
| 4. C2×Dic1076 | C2 | semidirect |
| 5. C2×#16864391 | C2 | semidirect |
| 6. C2×M16×C269 | C2 | semidirect |
| 13. C2×Dic538 | C22 | semidirect |
| 18. Dic1076 | C22 | semidirect |
| 19. #16864391 | C22 | semidirect |
| 21. M16×C269 | C22 | semidirect |
| 53. C2×C269 | #137 | semidirect |
| 56. C269 | C2×#137 | semidirect |
| 63. C2×M16 | D269 | semidirect |
| 78. M16 | C2×D269 | semidirect |
| 111. C2 | #22575486 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16864402 | 2 |
| C22×Dic538 | 2 |
| #22575486 | 2 |
| C2×Dic1076 | 2 |
| C2×#16864391 | 2 |
| C2×M16×C269 | 2 |
| C2×#137 | 269 |