Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
398 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 398 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 |
|---|---|---|
| 2. #11763289 | C2 | semidirect |
| 3. #11763148 | C2 | semidirect |
| 4. #11763138 | C2 | semidirect |
| 5. #11763132 | C2 | semidirect |
| 6. #11763126 | C2 | semidirect |
| 7. #11762852 | C2 | semidirect |
| 8. C2×#10587488 | C2 | semidirect |
| 9. #11762810 | C2 | semidirect |
| 10. #11762775 | C2 | semidirect |
| 11. C17×#416 | C2 | semidirect |
| 137. #416 | D17 | semidirect |
| 174. C17 | #3099 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763387 | 2 |
| #11763289 | 2 |
| #11763148 | 2 |
| #11763138 | 2 |
| #11763132 | 2 |
| #11763126 | 2 |
| #11762852 | 2 |
| C2×#10587488 | 2 |
| #11762810 | 2 |
| #11762775 | 2 |
| C17×#416 | 2 |
| #3099 | 17 |