Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
300 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 70 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×#10587536 | C2 | semidirect |
| 2. C2×#10587548 | C2 | semidirect |
| 3. #11763783 | C2 | semidirect |
| 4. C2×C8×#595 | C2 | semidirect |
| 10. C2×D8×C17 | C4 | semidirect |
| 11. C2×#63229 | C4 | semidirect |
| 14. C2×Dic68 | C4 | semidirect |
| 96. C2×D8 | #595 | semidirect |
| 105. C17 | #1974 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587536 | 2 |
| C2×#10587548 | 2 |
| #11763783 | 2 |
| C2×C8×#595 | 2 |
| C2×#10587598 | 2 |
| #1974 | 17 |