Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
404 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 123 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×#10587574 | C2 | semidirect |
| 3. #11763213 | C2 | semidirect |
| 4. #11763154 | C2 | semidirect |
| 5. #11763123 | C2 | semidirect |
| 6. #11763122 | C2 | semidirect |
| 7. #11763120 | C2 | semidirect |
| 8. #11763088 | C2 | semidirect |
| 9. #11763087 | C2 | semidirect |
| 10. #11762859 | C2 | semidirect |
| 11. C17×#480 | C2 | semidirect |
| 139. #480 | D17 | semidirect |
| 180. C17 | #3226 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763354 | 2 |
| C2×#10587574 | 2 |
| #11763213 | 2 |
| #11763154 | 2 |
| #11763123 | 2 |
| #11763122 | 2 |
| #11763120 | 2 |
| #11763088 | 2 |
| #11763087 | 2 |
| #11762859 | 2 |
| C17×#480 | 2 |
| #3226 | 17 |