Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
500 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 133 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×#10587628 | C2 | semidirect |
| 3. C2×#10587633 | C2 | semidirect |
| 4. #11763277 | C2 | semidirect |
| 5. #11763034 | C2 | semidirect |
| 6. #11763027 | C2 | semidirect |
| 7. #11762832 | C2 | semidirect |
| 8. #11762813 | C2 | semidirect |
| 9. C17×#419 | C2 | semidirect |
| 18. C2×#63231 | C22 | semidirect |
| 20. C2×#63230 | C22 | semidirect |
| 27. #10587579 | C22 | semidirect |
| 28. #10587573 | C22 | semidirect |
| 32. C17×#103 | C22 | semidirect |
| 33. #10587485 | C22 | semidirect |
| 128. #419 | D17 | semidirect |
| 158. #103 | C2×D17 | semidirect |
| 160. C17 | #3040 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587628 | 2 |
| C2×#10587594 | 2 |
| C2×#10587633 | 2 |
| #11763277 | 2 |
| #11763034 | 2 |
| #11763027 | 2 |
| #11762832 | 2 |
| #11762813 | 2 |
| C17×#419 | 2 |
| #3040 | 17 |