Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
656 conjugacy classes of subgroups; only the 218 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 218 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. #11763760 | C2 | semidirect |
| 5. C4×C4⋊#595 | C2 | semidirect |
| 17. C17×#117 | C4 | semidirect |
| 18. #10587612 | C4 | semidirect |
| 19. #10587578 | C4 | semidirect |
| 22. #10587563 | C4 | semidirect |
| 23. #10587558 | C4 | semidirect |
| 46. C4⋊C4×C17 | C2×C4 | semidirect |
| 48. C42×C17 | C2×C4 | semidirect |
| 51. C4⋊Dic17 | C2×C4 | semidirect |
| 52. #63225 | C2×C4 | semidirect |
| 53. C4×Dic17 | C2×C4 | semidirect |
| 54. C4×Dic17 | C2×C4 | semidirect |
| 67. C2×C4×C17 | C4⋊C4 | semidirect |
| 71. C2×Dic17 | C4⋊C4 | semidirect |
| 76. C4×D17 | C4⋊C4 | semidirect |
| 77. C4×D17 | C4⋊C4 | semidirect |
| 120. #117 | #595 | semidirect |
| 132. C17 | #2296 | semidirect |
| 151. C4⋊C4 | C2×#595 | semidirect |
| 161. C42 | C2×#595 | 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×#10587677 | 2 |
| C22×C4×#595 | 2 |
| #11763760 | 2 |
| #11763756 | 2 |
| C4×C4⋊#595 | 2 |
| #117×D17 | 2 |
| #2296 | 17 |