Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
446 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 446 conjugacy classes of subgroups — too many to draw. Only its 129 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×#10587595 | C2 | semidirect |
| 3. C2×#10587637 | C2 | semidirect |
| 4. #11763575 | C2 | semidirect |
| 5. #11763083 | C2 | semidirect |
| 6. #11763071 | C2 | semidirect |
| 7. #11762857 | C2 | semidirect |
| 8. C2×#10587495 | C2 | semidirect |
| 9. C17×#413 | C2 | semidirect |
| 20. C2×#63231 | C22 | semidirect |
| 22. C2×#63229 | C22 | semidirect |
| 33. C17×#101 | C22 | semidirect |
| 34. C17×#100 | C22 | semidirect |
| 35. #10587495 | C22 | semidirect |
| 36. #10587493 | C22 | semidirect |
| 144. #413 | D17 | semidirect |
| 177. #101 | C2×D17 | semidirect |
| 178. #100 | C2×D17 | semidirect |
| 179. C17 | #3069 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763607 | 2 |
| C2×#10587595 | 2 |
| C2×#10587637 | 2 |
| #11763575 | 2 |
| #11763083 | 2 |
| #11763071 | 2 |
| #11762857 | 2 |
| C2×#10587495 | 2 |
| C17×#413 | 2 |
| #3069 | 17 |