Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
380 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 88 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. C2×#10587549 | C2 | semidirect |
| 4. #11763682 | C2 | semidirect |
| 14. C17×C22⋊Q8 | C4 | semidirect |
| 15. #10587632 | C4 | semidirect |
| 16. #10587610 | C4 | semidirect |
| 17. #10587583 | C4 | semidirect |
| 98. C22×C17 | #103 | semidirect |
| 104. C2×D17 | #103 | semidirect |
| 142. C22⋊Q8 | #595 | semidirect |
| 150. C17 | #1892 | semidirect |
| 232. C22 | #10587549 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#63242 | 2 |
| C2×#10587549 | 2 |
| #11763751 | 2 |
| #11763682 | 2 |
| C22⋊Q8×D17 | 2 |
| #1892 | 17 |