Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
304 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 3. #11762817 | C2 | semidirect |
| 4. C2×#10587495 | C2 | semidirect |
| 5. #11762579 | C2 | semidirect |
| 6. #11762567 | C2 | semidirect |
| 16. C2×#63231 | C4 | semidirect |
| 17. C2×#63229 | C4 | semidirect |
| 132. C17 | #1902 | 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 |
| #11762817 | 2 |
| C2×#10587495 | 2 |
| #11762579 | 2 |
| #11762567 | 2 |
| C17×#421 | 2 |
| #1902 | 17 |