Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
740 conjugacy classes of subgroups; only the 170 normal subgroups are shown.
This group has 740 conjugacy classes of subgroups — too many to draw. Only its 170 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 |
|---|---|---|
| 1. C2×D4×#595 | C2 | semidirect |
| 2. #11763761 | C2 | semidirect |
| 3. #11763757 | C2 | semidirect |
| 4. #11763753 | C2 | semidirect |
| 5. #11763745 | C2 | semidirect |
| 16. C17×#127 | C4 | semidirect |
| 17. #10587626 | C4 | semidirect |
| 18. #10587626 | C4 | semidirect |
| 19. #10587560 | C4 | semidirect |
| 29. C2×D4×C17 | C2×C4 | semidirect |
| 30. C2×D4×C17 | C2×C4 | semidirect |
| 31. C2×C22⋊D17 | C2×C4 | semidirect |
| 32. C2×C22⋊D17 | C2×C4 | semidirect |
| 36. C2×D68 | C2×C4 | semidirect |
| 37. C2×D68 | C2×C4 | semidirect |
| 44. C4×#595 | D4 | semidirect |
| 45. C42×C17 | C2×C4 | semidirect |
| 46. C4×Dic17 | C2×C4 | semidirect |
| 47. C4×Dic17 | C2×C4 | semidirect |
| 112. #127 | #595 | semidirect |
| 122. C17 | #2328 | semidirect |
| 131. C2×D4 | C2×#595 | semidirect |
| 132. C2×D4 | C2×#595 | semidirect |
| 147. C42 | C2×#595 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×#595 | 2 |
| #11763761 | 2 |
| #11763757 | 2 |
| #11763753 | 2 |
| #11763745 | 2 |
| #127×D17 | 2 |
| #2328 | 17 |