Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
468 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 468 conjugacy classes of subgroups — too many to draw. Only its 133 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. C2×#10587595 | C2 | semidirect |
| 3. C22×#63229 | C2 | semidirect |
| 4. C2×#10587593 | C2 | semidirect |
| 5. #11763071 | C2 | direct (N × H) |
| 6. C2×#10587493 | C2 | semidirect |
| 7. C2×#10587495 | C2 | semidirect |
| 8. C2×C17×#100 | C2 | semidirect |
| 18. C2×#63229 | C22 | semidirect |
| 25. #10587595 | C22 | semidirect |
| 27. #10587593 | C22 | semidirect |
| 32. C17×#100 | C22 | semidirect |
| 33. #10587495 | C22 | semidirect |
| 34. #10587493 | C22 | semidirect |
| 140. C2×#100 | D17 | semidirect |
| 144. C2×C17 | #471 | semidirect |
| 172. #100 | C2×D17 | semidirect |
| 173. C17 | C2×#471 | semidirect |
| 275. C2 | #11763071 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587595 | 2 |
| C2×#10587618 | 2 |
| C22×#63229 | 2 |
| C2×#10587593 | 2 |
| #11763071 | 2 |
| C2×#10587493 | 2 |
| C2×#10587495 | 2 |
| C2×C17×#100 | 2 |
| C2×#471 | 17 |