Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
446 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 446 conjugacy classes of subgroups — too many to draw. Only its 137 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×#10587637 | C2 | semidirect |
| 2. C2×#10587637 | C2 | semidirect |
| 3. #11763576 | C2 | semidirect |
| 4. #11763082 | C2 | semidirect |
| 5. #11763070 | C2 | semidirect |
| 6. #11762857 | C2 | semidirect |
| 7. #11762793 | C2 | semidirect |
| 8. C2×#10587495 | C2 | semidirect |
| 26. C2×#63231 | C22 | semidirect |
| 28. C2×#63229 | C22 | semidirect |
| 33. #10587507 | C22 | semidirect |
| 34. #10587504 | C22 | semidirect |
| 35. #10587495 | C22 | semidirect |
| 36. #10587493 | C22 | semidirect |
| 179. C17 | #3069 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587637 | 2 |
| #11763576 | 2 |
| #11763082 | 2 |
| #11763070 | 2 |
| #11762857 | 2 |
| #11762793 | 2 |
| C2×#10587495 | 2 |
| C17×#575 | 2 |
| #3069 | 17 |