Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
728 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 728 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 |
|---|---|---|
| 1. C2×#10587697 | C2 | semidirect |
| 2. C2×#10587594 | C2 | semidirect |
| 3. C2×#10587635 | C2 | semidirect |
| 4. C2×#10587561 | C2 | semidirect |
| 5. #11762983 | C2 | direct (N × H) |
| 6. C2×#10587476 | C2 | semidirect |
| 7. C2×#10587495 | C2 | semidirect |
| 8. C2×C17×#104 | C2 | semidirect |
| 13. #10587697 | C22 | semidirect |
| 25. #10587635 | C22 | semidirect |
| 31. #10587594 | C22 | semidirect |
| 35. #10587561 | C22 | semidirect |
| 36. C17×#104 | C22 | semidirect |
| 37. #10587495 | C22 | semidirect |
| 38. #10587476 | C22 | semidirect |
| 175. C2×#104 | D17 | semidirect |
| 180. C2×C17 | #454 | semidirect |
| 212. #104 | C2×D17 | semidirect |
| 214. C17 | C2×#454 | semidirect |
| 349. C2 | #11762983 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587697 | 2 |
| C2×#10587594 | 2 |
| C2×#10587635 | 2 |
| C2×#10587561 | 2 |
| #11762983 | 2 |
| C2×#10587476 | 2 |
| C2×#10587495 | 2 |
| C2×C17×#104 | 2 |
| C2×#454 | 17 |