Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
326 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 69 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. #11762851 | C2 | semidirect |
| 3. #11762810 | C2 | semidirect |
| 4. C2×#10587494 | C2 | semidirect |
| 5. #11762711 | C2 | semidirect |
| 6. #11762569 | C2 | semidirect |
| 7. C2×C17×#104 | C2 | semidirect |
| 48. M16×C17 | D4 | semidirect |
| 126. C2×#104 | D17 | semidirect |
| 157. C17 | #2037 | semidirect |
| 181. M16 | C22⋊D17 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763373 | 2 |
| #11762851 | 2 |
| #11762810 | 2 |
| C2×#10587494 | 2 |
| #11762711 | 2 |
| #11762569 | 2 |
| C2×C17×#104 | 2 |
| #2037 | 17 |