Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
280 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 80 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 |
|---|---|---|
| 1. C2×#10587544 | C2 | semidirect |
| 4. C2×#10587542 | C2 | semidirect |
| 5. #11763675 | C2 | semidirect |
| 6. #11763675 | C2 | semidirect |
| 145. C17 | #1924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587544 | 2 |
| C2×#10587543 | 2 |
| C2×#10587542 | 2 |
| #11763675 | 2 |
| #11762656 | 2 |
| #1924 | 17 |