Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
376 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 141 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. #11763440 | C2 | semidirect |
| 3. #11763114 | C2 | semidirect |
| 4. #11763111 | C2 | semidirect |
| 5. #11763102 | C2 | semidirect |
| 6. #11763087 | C2 | semidirect |
| 7. #11762851 | C2 | semidirect |
| 8. C2×#10587478 | C2 | semidirect |
| 9. #11762837 | C2 | semidirect |
| 42. #41×C17 | Q8 | semidirect |
| 164. C17 | #3083 | semidirect |
| 166. #41 | Dic34 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763440 | 2 |
| #11763292 | 2 |
| #11763114 | 2 |
| #11763111 | 2 |
| #11763102 | 2 |
| #11763087 | 2 |
| #11762851 | 2 |
| C2×#10587478 | 2 |
| #11762837 | 2 |
| #11762805 | 2 |
| C17×#417 | 2 |
| #3083 | 17 |