Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
752 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 752 conjugacy classes of subgroups — too many to draw. Only its 149 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. C22×#63230 | C2 | semidirect |
| 3. #11763383 | C2 | semidirect |
| 4. #11762970 | C2 | semidirect |
| 5. #11762958 | C2 | semidirect |
| 6. #11762815 | C2 | semidirect |
| 7. #11762805 | C2 | semidirect |
| 8. #11762777 | C2 | semidirect |
| 9. C2×C17×#137 | C2 | semidirect |
| 11. C22×Q8×C17 | C22 | semidirect |
| 22. C2×Q16×C17 | C22 | semidirect |
| 23. C2×SD16×C17 | C22 | semidirect |
| 24. C2×M16×C17 | C22 | semidirect |
| 26. #10587632 | C22 | semidirect |
| 29. C2×#63230 | C22 | semidirect |
| 31. #10587612 | C22 | semidirect |
| 32. C22×#3622 | C22 | semidirect |
| 33. #10587506 | C22 | semidirect |
| 34. #10587503 | C22 | semidirect |
| 35. #10587492 | C22 | semidirect |
| 36. #10587491 | C22 | semidirect |
| 142. C2×#137 | D17 | semidirect |
| 162. C22×Q8 | C2×D17 | semidirect |
| 168. C2×Q16 | C2×D17 | semidirect |
| 171. C2×SD16 | C2×D17 | semidirect |
| 172. C2×M16 | C2×D17 | semidirect |
| 183. C17 | #3009 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587696 | 2 |
| C22×#63230 | 2 |
| #11763383 | 2 |
| #11762970 | 2 |
| #11762958 | 2 |
| #11762815 | 2 |
| #11762805 | 2 |
| #11762777 | 2 |
| C2×C17×#137 | 2 |
| #3009 | 17 |