Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
520 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 129 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×#10587594 | C2 | semidirect |
| 2. #11763455 | C2 | semidirect |
| 3. #11763193 | C2 | semidirect |
| 4. #11763055 | C2 | semidirect |
| 5. #11763025 | C2 | semidirect |
| 6. #11762973 | C2 | semidirect |
| 7. #11762945 | C2 | semidirect |
| 8. C4×D136 | C2 | semidirect |
| 9. C17×#436 | C2 | semidirect |
| 11. C22×D68 | C22 | semidirect |
| 12. C2×M16×C17 | C22 | semidirect |
| 16. #10587610 | C22 | semidirect |
| 18. C2×Dic68 | C22 | semidirect |
| 22. C2×#63219 | C22 | semidirect |
| 23. C2×#63219 | C22 | semidirect |
| 27. #10587561 | C22 | semidirect |
| 28. C4×D68 | C22 | semidirect |
| 29. C17×C4⋊C8 | C22 | semidirect |
| 30. C17×C22⋊C8 | C22 | semidirect |
| 31. C4×C8×C17 | C22 | semidirect |
| 32. #10587492 | C22 | semidirect |
| 33. #10587492 | C22 | semidirect |
| 34. #10587489 | C22 | semidirect |
| 35. #10587487 | C22 | semidirect |
| 68. D136 | D4 | semidirect |
| 127. #436 | D17 | semidirect |
| 143. C2×M16 | C2×D17 | semidirect |
| 154. C4⋊C8 | C2×D17 | semidirect |
| 158. C22⋊C8 | C2×D17 | semidirect |
| 159. C4×C8 | C2×D17 | semidirect |
| 160. C17 | #3273 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587594 | 2 |
| #11763455 | 2 |
| #11763193 | 2 |
| #11763055 | 2 |
| #11763025 | 2 |
| #11762973 | 2 |
| #11762945 | 2 |
| C4×D136 | 2 |
| C17×#436 | 2 |
| #3273 | 17 |