Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
484 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 157 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 |
|---|---|---|
| 4. #11762715 | C2 | semidirect |
| 5. #11762715 | C2 | semidirect |
| 6. #11762694 | C2 | semidirect |
| 7. #11762679 | C2 | semidirect |
| 8. #11762675 | C2 | semidirect |
| 137. C17 | #2499 | semidirect |
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 |
| #11762734 | 2 |
| #11762715 | 2 |
| #11762694 | 2 |
| #11762679 | 2 |
| #11762675 | 2 |
| C4×C22⋊C4×C17 | 2 |
| #2499 | 17 |