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. C2×#10587496 | C2 | semidirect |
| 4. #11762811 | C2 | semidirect |
| 5. #11762712 | C2 | semidirect |
| 6. #11762570 | C2 | semidirect |
| 7. C2×C17×#100 | C2 | semidirect |
| 50. M16×C17 | D4 | semidirect |
| 128. C2×#100 | 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 |
|---|---|
| #11763376 | 2 |
| #11762851 | 2 |
| C2×#10587496 | 2 |
| #11762811 | 2 |
| #11762712 | 2 |
| #11762570 | 2 |
| C2×C17×#100 | 2 |
| #2037 | 17 |