Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
416 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 149 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. #11763151 | C2 | direct (N × H) |
| 4. C2×#10587489 | C2 | semidirect |
| 5. C2×#10587488 | C2 | semidirect |
| 6. C2×#10587487 | C2 | semidirect |
| 7. C2×#10587487 | C2 | semidirect |
| 25. #10587489 | C22 | semidirect |
| 26. #10587488 | C22 | semidirect |
| 27. #10587487 | C22 | semidirect |
| 28. #10587487 | C22 | semidirect |
| 111. C2×C17 | #485 | semidirect |
| 135. C17 | C2×#485 | semidirect |
| 209. C2 | #11763151 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587610 | 2 |
| C2×#10587612 | 2 |
| #11763151 | 2 |
| C2×#10587489 | 2 |
| C2×#10587488 | 2 |
| C2×#10587487 | 2 |
| C2×C17×C22⋊C8 | 2 |
| C2×#485 | 17 |