Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
364 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 364 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. #11763523 | C2 | semidirect |
| 2. #11763213 | C2 | semidirect |
| 3. #11763132 | C2 | semidirect |
| 4. #11763130 | C2 | semidirect |
| 5. #11763097 | C2 | semidirect |
| 6. #11763042 | C2 | semidirect |
| 7. D8×Dic17 | C2 | semidirect |
| 8. C8×C22⋊D17 | C2 | semidirect |
| 9. #11762847 | C2 | semidirect |
| 10. #11762846 | C2 | semidirect |
| 11. C17×#466 | C2 | semidirect |
| 121. #466 | D17 | semidirect |
| 159. C17 | #3341 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763523 | 2 |
| #11763213 | 2 |
| #11763132 | 2 |
| #11763130 | 2 |
| #11763097 | 2 |
| #11763042 | 2 |
| D8×Dic17 | 2 |
| C8×C22⋊D17 | 2 |
| #11762847 | 2 |
| #11762846 | 2 |
| C17×#466 | 2 |
| #3341 | 17 |