Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
458 conjugacy classes of subgroups; only the 217 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 217 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. #11763576 | C2 | semidirect |
| 2. #11762931 | C2 | semidirect |
| 3. #11762926 | C2 | semidirect |
| 4. #11762858 | C2 | semidirect |
| 5. C2×#10587508 | C2 | semidirect |
| 6. M16×Dic17 | C2 | semidirect |
| 9. C17×#137 | C4 | semidirect |
| 10. C17×AGL(1,ℤ/8) | C4 | semidirect |
| 14. #10587634 | C22 | semidirect |
| 19. #10587508 | C22 | semidirect |
| 20. #10587508 | C22 | semidirect |
| 21. #10587490 | C22 | semidirect |
| 22. #10587486 | C22 | semidirect |
| 23. C8×Dic17 | C22 | semidirect |
| 34. Q16×C17 | C2×C4 | semidirect |
| 35. SD16×C17 | C2×C4 | semidirect |
| 36. D8×C17 | C2×C4 | semidirect |
| 94. #137 | Dic17 | semidirect |
| 95. AGL(1,ℤ/8) | Dic17 | semidirect |
| 109. C17 | #2956 | semidirect |
| 120. Q16 | C2×Dic17 | semidirect |
| 121. SD16 | C2×Dic17 | semidirect |
| 122. D8 | C2×Dic17 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763576 | 2 |
| #11762931 | 2 |
| #11762926 | 2 |
| #11762858 | 2 |
| C2×#10587508 | 2 |
| M16×Dic17 | 2 |
| C17×#575 | 2 |
| #2956 | 17 |