Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
362 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 115 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. #11763426 | C2 | semidirect |
| 2. #11763213 | C2 | semidirect |
| 3. #11763192 | C2 | semidirect |
| 4. #11763167 | C2 | semidirect |
| 5. #11763053 | C2 | semidirect |
| 6. #11763050 | C2 | semidirect |
| 7. #11762906 | C2 | semidirect |
| 8. #11762903 | C2 | semidirect |
| 9. D8×Dic17 | C2 | semidirect |
| 10. #11762764 | C2 | semidirect |
| 156. C17 | #3175 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763426 | 2 |
| #11763213 | 2 |
| #11763192 | 2 |
| #11763167 | 2 |
| #11763053 | 2 |
| #11763050 | 2 |
| #11762906 | 2 |
| #11762903 | 2 |
| D8×Dic17 | 2 |
| #11762764 | 2 |
| C17×#466 | 2 |
| #3175 | 17 |