Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
468 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 468 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. C22×#63230 | C2 | semidirect |
| 3. C2×#10587634 | C2 | semidirect |
| 4. #11763074 | C2 | direct (N × H) |
| 5. C2×#10587493 | C2 | semidirect |
| 6. C2×#10587507 | C2 | semidirect |
| 7. C2×#10587494 | C2 | semidirect |
| 8. C2×C17×#137 | C2 | semidirect |
| 13. C17×#137 | C22 | semidirect |
| 20. #10587634 | C22 | semidirect |
| 25. C2×#63230 | C22 | semidirect |
| 32. #10587507 | C22 | semidirect |
| 33. #10587494 | C22 | semidirect |
| 34. #10587493 | C22 | semidirect |
| 133. C2×#137 | D17 | semidirect |
| 144. C2×C17 | #471 | semidirect |
| 151. #137 | C2×D17 | semidirect |
| 173. C17 | C2×#471 | semidirect |
| 275. C2 | #11763074 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587635 | 2 |
| C22×#63230 | 2 |
| C2×#10587634 | 2 |
| #11763074 | 2 |
| C2×#10587493 | 2 |
| C2×#10587507 | 2 |
| C2×#10587494 | 2 |
| C2×C17×#137 | 2 |
| C2×#471 | 17 |