Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
788 conjugacy classes of subgroups; only the 202 normal subgroups are shown.
This group has 788 conjugacy classes of subgroups — too many to draw. Only its 202 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×#10587677 | C2 | semidirect |
| 2. #11763790 | C2 | direct (N × H) |
| 3. C2×#10587539 | C2 | semidirect |
| 5. C22×Q8×C17 | C4 | semidirect |
| 9. C2×#63256 | C4 | semidirect |
| 11. C22×D68 | C4 | semidirect |
| 13. C22×C4×D17 | C4 | semidirect |
| 17. #10587677 | C22 | semidirect |
| 20. #10587539 | C22 | semidirect |
| 26. C2×Q8×C17 | C2×C4 | semidirect |
| 39. C2×D68 | C2×C4 | semidirect |
| 45. C2×C4×D17 | C2×C4 | semidirect |
| 112. C2×C17 | #410 | semidirect |
| 122. C22×Q8 | #595 | semidirect |
| 133. C17 | C2×#410 | semidirect |
| 142. C2×Q8 | C2×#595 | semidirect |
| 223. C2 | #11763790 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587677 | 2 |
| #11763790 | 2 |
| C2×#10587539 | 2 |
| C22×#63256 | 2 |
| C2×#410 | 17 |