Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
368 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 69 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×#10587505 | C2 | semidirect |
| 3. #11762601 | C2 | direct (N × H) |
| 4. C2×C17×#99 | C2 | semidirect |
| 8. C22×D68 | C4 | semidirect |
| 13. #10587626 | C4 | semidirect |
| 15. C2×C4×Dic17 | C4 | semidirect |
| 17. C17×#99 | C22 | semidirect |
| 19. #10587505 | C22 | semidirect |
| 42. C2×D68 | C2×C4 | semidirect |
| 48. C4×Dic17 | C2×C4 | semidirect |
| 114. C2×#99 | D17 | semidirect |
| 122. C2×C17 | #353 | semidirect |
| 139. #99 | C2×D17 | semidirect |
| 140. C17 | C2×#353 | semidirect |
| 239. C2 | #11762601 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587626 | 2 |
| C2×#10587505 | 2 |
| #11762601 | 2 |
| C2×C17×#99 | 2 |
| C2×#353 | 17 |