Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
484 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 143 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×Q8×Dic17 | C2 | semidirect |
| 4. #11763033 | C2 | semidirect |
| 5. #11763029 | C2 | semidirect |
| 6. #11763017 | C2 | semidirect |
| 7. #11763007 | C2 | semidirect |
| 8. #11762832 | C2 | semidirect |
| 9. #11762811 | C2 | semidirect |
| 10. #11762810 | C2 | semidirect |
| 11. C2×C17×#137 | C2 | semidirect |
| 49. C2×Q8×C17 | D4 | semidirect |
| 151. Dic17 | #137 | semidirect |
| 153. C2×#137 | D17 | semidirect |
| 202. C17 | #3037 | semidirect |
| 210. C2×Q8 | C22⋊D17 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587628 | 2 |
| #11763355 | 2 |
| C2×Q8×Dic17 | 2 |
| #11763033 | 2 |
| #11763029 | 2 |
| #11763017 | 2 |
| #11763007 | 2 |
| #11762832 | 2 |
| #11762811 | 2 |
| #11762810 | 2 |
| C2×C17×#137 | 2 |
| #3037 | 17 |