Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
472 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 472 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 |
|---|---|---|
| 1. C2×#10587628 | C2 | semidirect |
| 3. #11763289 | C2 | semidirect |
| 4. #11763028 | C2 | semidirect |
| 5. #11763021 | C2 | semidirect |
| 6. #11763016 | C2 | semidirect |
| 7. #11763011 | C2 | semidirect |
| 8. #11762836 | C2 | semidirect |
| 9. #11762810 | C2 | semidirect |
| 10. C2×#10587506 | C2 | semidirect |
| 11. C17×#536 | C2 | semidirect |
| 143. #536 | D17 | semidirect |
| 189. C17 | #3046 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587628 | 2 |
| C2×#10587636 | 2 |
| #11763289 | 2 |
| #11763028 | 2 |
| #11763021 | 2 |
| #11763016 | 2 |
| #11763011 | 2 |
| #11762836 | 2 |
| #11762810 | 2 |
| C2×#10587506 | 2 |
| C17×#536 | 2 |
| #3046 | 17 |