Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
392 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 392 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 |
|---|---|---|
| 2. C2×#10587576 | C2 | semidirect |
| 3. #11763176 | C2 | semidirect |
| 4. #11763172 | C2 | semidirect |
| 5. #11763165 | C2 | semidirect |
| 6. #11763162 | C2 | semidirect |
| 7. #11762811 | C2 | semidirect |
| 8. #11762810 | C2 | semidirect |
| 9. #11762808 | C2 | semidirect |
| 10. M16×Dic17 | C2 | semidirect |
| 11. C17×#417 | C2 | semidirect |
| 150. #417 | D17 | semidirect |
| 189. C17 | #3142 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763355 | 2 |
| C2×#10587576 | 2 |
| #11763176 | 2 |
| #11763172 | 2 |
| #11763165 | 2 |
| #11763162 | 2 |
| #11762811 | 2 |
| #11762810 | 2 |
| #11762808 | 2 |
| M16×Dic17 | 2 |
| C17×#417 | 2 |
| #3142 | 17 |