Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
756 conjugacy classes of subgroups; only the 249 normal subgroups are shown.
This group has 756 conjugacy classes of subgroups — too many to draw. Only its 249 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 |
|---|---|---|
| 2. #11763576 | C2 | semidirect |
| 3. #11762791 | C2 | semidirect |
| 4. C2×#10587494 | C2 | semidirect |
| 5. C17×#568 | C2 | semidirect |
| 14. C2×M16×C17 | C22 | semidirect |
| 16. C2×#63223 | C22 | semidirect |
| 17. #10587495 | C22 | semidirect |
| 18. #10587494 | C22 | semidirect |
| 75. #568 | D17 | semidirect |
| 92. C2×M16 | C2×D17 | semidirect |
| 95. C17 | #2888 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587696 | 2 |
| #11763576 | 2 |
| #11762791 | 2 |
| C2×#10587494 | 2 |
| C17×#568 | 2 |
| #2888 | 17 |