Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
380 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 78 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. #11763751 | C2 | semidirect |
| 3. #11763687 | C2 | semidirect |
| 6. C22×C4×D17 | C4 | semidirect |
| 10. C2×C4⋊C4×C17 | C4 | semidirect |
| 11. C2×#63227 | C4 | semidirect |
| 13. C2×C4×Dic17 | C4 | semidirect |
| 51. C22×D17 | C4⋊C4 | semidirect |
| 65. C2×C4×C17 | C4⋊C4 | semidirect |
| 101. Dic17 | #99 | semidirect |
| 120. C2×C4⋊C4 | #595 | semidirect |
| 127. C17 | #1799 | semidirect |
| 185. C2×C4 | C4⋊#595 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587539 | 2 |
| #11763751 | 2 |
| #11763687 | 2 |
| C2×#10587579 | 2 |
| #1799 | 17 |