Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
160 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 78 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 |
|---|---|---|
| 3. #11763700 | C2 | semidirect |
| 4. #11763699 | C2 | semidirect |
| 9. #10587538 | C4 | semidirect |
| 13. #10587529 | C4 | semidirect |
| 14. C2×C16×C17 | C4 | semidirect |
| 15. C2×#63214 | C4 | semidirect |
| 16. #10587469 | C4 | semidirect |
| 17. #10587469 | C4 | semidirect |
| 81. C2×C16 | #595 | semidirect |
| 84. C17 | #2110 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763865 | 2 |
| #11763772 | 2 |
| #11763700 | 2 |
| #11763699 | 2 |
| C2×#10587469 | 2 |
| #2110 | 17 |