Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
588 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 588 conjugacy classes of subgroups — too many to draw. Only its 97 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. #11762826 | C2 | semidirect |
| 3. #11762815 | C2 | semidirect |
| 4. #11762813 | C2 | semidirect |
| 5. #11762791 | C2 | semidirect |
| 6. #11762782 | C2 | semidirect |
| 7. C17×#421 | C2 | semidirect |
| 13. C2×#63256 | C4 | semidirect |
| 15. C2×D4×D17 | C4 | semidirect |
| 20. C2×M16×C17 | C22 | semidirect |
| 21. C17×#117 | C22 | semidirect |
| 22. #10587612 | C22 | semidirect |
| 23. C2×#63223 | C22 | semidirect |
| 149. #421 | D17 | semidirect |
| 174. C2×M16 | C2×D17 | semidirect |
| 176. #117 | C2×D17 | semidirect |
| 184. C17 | #1795 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587696 | 2 |
| #11762826 | 2 |
| #11762815 | 2 |
| #11762813 | 2 |
| #11762791 | 2 |
| #11762782 | 2 |
| C17×#421 | 2 |
| #1795 | 17 |