Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
774 conjugacy classes of subgroups; only the 206 normal subgroups are shown.
This group has 774 conjugacy classes of subgroups — too many to draw. Only its 206 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×#10587680 | C2 | semidirect |
| 2. #11763784 | C2 | semidirect |
| 3. #11763780 | C2 | semidirect |
| 4. #11763777 | C2 | semidirect |
| 15. C2×#63243 | C22 | semidirect |
| 16. C2×#63242 | C22 | semidirect |
| 19. #10587543 | C22 | semidirect |
| 20. #10587543 | C22 | semidirect |
| 70. C22×C17 | #131 | semidirect |
| 109. C17 | #2880 | semidirect |
| 165. C22 | #10587680 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587680 | 2 |
| #11763784 | 2 |
| #11763780 | 2 |
| #11763777 | 2 |
| C22×#63256 | 2 |
| #2880 | 17 |