Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
816 conjugacy classes of subgroups; only the 210 normal subgroups are shown.
This group has 816 conjugacy classes of subgroups — too many to draw. Only its 210 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. #11763756 | C2 | semidirect |
| 3. #11763751 | C2 | semidirect |
| 11. C2×C4⋊#595 | C22 | semidirect |
| 12. C2×C22⋊C4×C17 | C4 | semidirect |
| 13. C2×C22⋊Dic17 | C4 | semidirect |
| 14. C2×#63227 | C4 | semidirect |
| 15. C22⋊C4×D17 | C4 | semidirect |
| 17. (C2×#595)⋊C4 | C22 | semidirect |
| 29. C22×C4×C17 | C2×C4 | semidirect |
| 30. C22×Dic17 | C2×C4 | semidirect |
| 32. C2×C4×D17 | C2×C4 | semidirect |
| 37. C22⋊C4×C17 | C2×C4 | semidirect |
| 38. C22⋊Dic17 | C2×C4 | semidirect |
| 39. #63227 | C2×C4 | semidirect |
| 41. C23×C17 | C4⋊C4 | semidirect |
| 50. C22×D17 | C4⋊C4 | semidirect |
| 51. C22×D17 | C4⋊C4 | semidirect |
| 114. C2×C22⋊C4 | #595 | semidirect |
| 116. C17 | #2315 | semidirect |
| 132. C22×C4 | C2×#595 | semidirect |
| 138. C22⋊C4 | C2×#595 | semidirect |
| 155. C23 | C4⋊#595 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C22⋊#595 | 2 |
| #11763756 | 2 |
| #11763751 | 2 |
| C2×C22⋊C4×D17 | 2 |
| #2315 | 17 |