Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
280 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 141 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 |
|---|---|---|
| 12. C17×#106 | C4 | semidirect |
| 14. #10587488 | C4 | semidirect |
| 15. C8×Dic17 | C4 | semidirect |
| 51. C8×C17 | C42 | semidirect |
| 66. Dic17 | #106 | direct (N × H) |
| 84. #106 | Dic17 | direct (N × H) |
| 87. C17 | C4×#106 | semidirect |
| 124. C8 | C4×Dic17 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587488 | 2 |
| C2×C8×Dic17 | 2 |
| C4⋊C4×Dic17 | 2 |
| #11762571 | 2 |
| C2×C17×#106 | 2 |
| C4×#106 | 17 |