Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
264 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 93 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. C2×#10587493 | C2 | semidirect |
| 3. C2×#10587478 | C2 | semidirect |
| 5. #11762578 | C2 | semidirect |
| 6. #11762577 | C2 | semidirect |
| 12. #10587634 | C4 | semidirect |
| 129. C17 | #1816 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587634 | 2 |
| C2×#10587493 | 2 |
| C2×#10587478 | 2 |
| #11762810 | 2 |
| #11762578 | 2 |
| #11762577 | 2 |
| C17×#417 | 2 |
| #1816 | 17 |