Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
196 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 129 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. #11762584 | C2 | semidirect |
| 4. C16×Dic17 | C2 | semidirect |
| 9. C17×M32 | C4 | semidirect |
| 15. #10587483 | C4 | semidirect |
| 29. C16×C17 | C2×C4 | semidirect |
| 30. #63214 | C2×C4 | semidirect |
| 52. Dic17 | M32 | direct (N × H) |
| 65. M32 | Dic17 | direct (N × H) |
| 72. C17 | C4×M32 | semidirect |
| 86. C16 | C2×Dic17 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587483 | 2 |
| C2×C8×Dic17 | 2 |
| #11762584 | 2 |
| C16×Dic17 | 2 |
| C2×C17×M32 | 2 |
| C4×M32 | 17 |