Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
462 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 125 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×#10587610 | C2 | semidirect |
| 3. #11763145 | C2 | semidirect |
| 4. #11763123 | C2 | semidirect |
| 5. #11763055 | C2 | semidirect |
| 6. #11762962 | C2 | semidirect |
| 7. #11762950 | C2 | semidirect |
| 8. C17×#407 | C2 | semidirect |
| 12. C22×Dic34 | C22 | semidirect |
| 13. C2×M16×C17 | C22 | semidirect |
| 21. C2×C4⋊Dic17 | C22 | semidirect |
| 25. #10587610 | C22 | semidirect |
| 27. C2×#63219 | C22 | semidirect |
| 29. C17×C22⋊C8 | C22 | semidirect |
| 30. #10587492 | C22 | semidirect |
| 31. #10587489 | C22 | semidirect |
| 32. #10587487 | C22 | semidirect |
| 130. #407 | D17 | semidirect |
| 143. C2×M16 | C2×D17 | semidirect |
| 161. C22⋊C8 | C2×D17 | semidirect |
| 162. C17 | #3193 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587610 | 2 |
| C2×#10587616 | 2 |
| #11763145 | 2 |
| #11763123 | 2 |
| #11763055 | 2 |
| #11762962 | 2 |
| #11762950 | 2 |
| C17×#407 | 2 |
| #3193 | 17 |