Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
500 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 141 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×#10587595 | C2 | semidirect |
| 3. C2×#10587561 | C2 | semidirect |
| 4. C4×#63252 | C2 | semidirect |
| 5. #11763032 | C2 | semidirect |
| 6. #11763025 | C2 | semidirect |
| 7. #11762819 | C2 | semidirect |
| 8. #11762815 | C2 | semidirect |
| 9. C17×#423 | C2 | semidirect |
| 21. C2×Dic68 | C22 | semidirect |
| 24. C2×#63219 | C22 | semidirect |
| 28. C4×D68 | C22 | semidirect |
| 31. C4×Dic34 | C22 | semidirect |
| 32. C17×C4⋊C8 | C22 | semidirect |
| 34. #10587487 | C22 | semidirect |
| 127. #423 | D17 | semidirect |
| 157. C4⋊C8 | C2×D17 | semidirect |
| 160. C17 | #3040 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587595 | 2 |
| C2×#10587594 | 2 |
| C2×#10587561 | 2 |
| C4×#63252 | 2 |
| #11763032 | 2 |
| #11763025 | 2 |
| #11762819 | 2 |
| #11762815 | 2 |
| C17×#423 | 2 |
| #3040 | 17 |