Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
386 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 3. #11763149 | C2 | semidirect |
| 4. #11763148 | C2 | semidirect |
| 5. #11763143 | C2 | semidirect |
| 6. #11763138 | C2 | semidirect |
| 7. #11762851 | C2 | semidirect |
| 8. #11762845 | C2 | semidirect |
| 9. C2×#10587506 | C2 | semidirect |
| 11. C17×#419 | C2 | semidirect |
| 130. #419 | D17 | semidirect |
| 167. C17 | #3097 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763383 | 2 |
| #11763289 | 2 |
| #11763149 | 2 |
| #11763148 | 2 |
| #11763143 | 2 |
| #11763138 | 2 |
| #11762851 | 2 |
| #11762845 | 2 |
| C2×#10587506 | 2 |
| #11762777 | 2 |
| C17×#419 | 2 |
| #3097 | 17 |