Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
752 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 752 conjugacy classes of subgroups — too many to draw. Only its 149 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. C2×#10587595 | C2 | semidirect |
| 3. C22×#63219 | C2 | semidirect |
| 4. #11763380 | C2 | semidirect |
| 5. #11762973 | C2 | semidirect |
| 6. #11762962 | C2 | semidirect |
| 7. #11762815 | C2 | semidirect |
| 8. #11762806 | C2 | semidirect |
| 9. C17×#408 | C2 | semidirect |
| 20. C22×Dic34 | C22 | semidirect |
| 21. C2×M16×C17 | C22 | semidirect |
| 22. C22×C8×C17 | C22 | semidirect |
| 26. #10587612 | C22 | semidirect |
| 27. #10587610 | C22 | semidirect |
| 29. C2×Dic68 | C22 | semidirect |
| 31. C2×#63219 | C22 | semidirect |
| 32. C2×#63219 | C22 | semidirect |
| 33. C17×C22⋊C8 | C22 | semidirect |
| 34. #10587492 | C22 | semidirect |
| 35. #10587492 | C22 | semidirect |
| 36. #10587487 | C22 | semidirect |
| 149. #408 | D17 | semidirect |
| 172. C2×M16 | C2×D17 | semidirect |
| 173. C22×C8 | C2×D17 | semidirect |
| 182. C22⋊C8 | C2×D17 | semidirect |
| 183. C17 | #3009 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587696 | 2 |
| C2×#10587595 | 2 |
| C22×#63219 | 2 |
| #11763380 | 2 |
| #11762973 | 2 |
| #11762962 | 2 |
| #11762815 | 2 |
| #11762806 | 2 |
| C17×#408 | 2 |
| #3009 | 17 |