Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
472 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 472 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 |
|---|---|---|
| 2. #11763383 | C2 | semidirect |
| 3. #11763292 | C2 | semidirect |
| 4. #11763033 | C2 | semidirect |
| 5. #11763026 | C2 | semidirect |
| 6. #11763017 | C2 | semidirect |
| 7. #11763012 | C2 | semidirect |
| 8. #11762837 | C2 | semidirect |
| 9. #11762811 | C2 | semidirect |
| 10. C2×#10587506 | C2 | semidirect |
| 11. C2×C17×#137 | C2 | semidirect |
| 141. C2×#137 | D17 | semidirect |
| 189. C17 | #3046 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587636 | 2 |
| #11763383 | 2 |
| #11763292 | 2 |
| #11763033 | 2 |
| #11763026 | 2 |
| #11763017 | 2 |
| #11763012 | 2 |
| #11762837 | 2 |
| #11762811 | 2 |
| C2×#10587506 | 2 |
| C2×C17×#137 | 2 |
| #3046 | 17 |