Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
388 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 109 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. #11763415 | C2 | semidirect |
| 2. #11763384 | C2 | semidirect |
| 3. #11763198 | C2 | semidirect |
| 4. #11763183 | C2 | semidirect |
| 5. #11763166 | C2 | semidirect |
| 6. #11763027 | C2 | semidirect |
| 7. #11763013 | C2 | semidirect |
| 8. #11762957 | C2 | semidirect |
| 9. #11762949 | C2 | semidirect |
| 10. #11762871 | C2 | semidirect |
| 11. C17×#491 | C2 | semidirect |
| 120. #491 | D17 | semidirect |
| 159. C17 | #3221 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763415 | 2 |
| #11763384 | 2 |
| #11763198 | 2 |
| #11763183 | 2 |
| #11763166 | 2 |
| #11763027 | 2 |
| #11763013 | 2 |
| #11762957 | 2 |
| #11762949 | 2 |
| #11762871 | 2 |
| C17×#491 | 2 |
| #3221 | 17 |