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 |
|---|---|---|
| 2. C2×#10587633 | C2 | semidirect |
| 3. #41×Dic17 | C2 | semidirect |
| 4. #11763033 | C2 | semidirect |
| 5. #11763026 | C2 | semidirect |
| 6. #11762832 | C2 | semidirect |
| 7. #11762818 | C2 | semidirect |
| 8. #11762815 | C2 | semidirect |
| 9. C2×C17×#137 | C2 | semidirect |
| 14. C2×Q16×C17 | C22 | semidirect |
| 15. C2×SD16×C17 | C22 | semidirect |
| 21. Q8×Dic17 | C22 | semidirect |
| 24. D4×Dic17 | C22 | semidirect |
| 32. #10587506 | C22 | semidirect |
| 34. #10587485 | C22 | semidirect |
| 121. C2×#137 | D17 | semidirect |
| 140. C2×Q16 | C2×D17 | semidirect |
| 142. C2×SD16 | 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×#10587635 | 2 |
| C2×#10587633 | 2 |
| #41×Dic17 | 2 |
| #11763033 | 2 |
| #11763026 | 2 |
| #11762832 | 2 |
| #11762818 | 2 |
| #11762815 | 2 |
| C2×C17×#137 | 2 |
| #3040 | 17 |