Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
556 conjugacy classes of subgroups; only the 373 normal subgroups are shown.
This group has 556 conjugacy classes of subgroups — too many to draw. Only its 373 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. #11762767 | C2 | semidirect |
| 4. #11762764 | C2 | semidirect |
| 5. M16×Dic17 | C2 | semidirect |
| 6. C2×#10587486 | C2 | semidirect |
| 9. C17×#131 | C4 | semidirect |
| 12. #10587634 | C4 | semidirect |
| 30. M16×C17 | C2×C4 | semidirect |
| 31. C2×C8×C17 | C2×C4 | semidirect |
| 39. #63223 | C2×C4 | semidirect |
| 40. C2×#3622 | C2×C4 | semidirect |
| 78. #131 | Dic17 | semidirect |
| 92. C17 | #2875 | semidirect |
| 100. M16 | C2×Dic17 | semidirect |
| 104. C2×C8 | C2×Dic17 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587634 | 2 |
| #41×Dic17 | 2 |
| #11762767 | 2 |
| #11762764 | 2 |
| M16×Dic17 | 2 |
| C2×#10587486 | 2 |
| C2×C17×#131 | 2 |
| #2875 | 17 |