Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
448 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 448 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 |
|---|---|---|
| 2. C22×Dic68 | C2 | semidirect |
| 3. #11763084 | C2 | direct (N × H) |
| 4. C2×#10587490 | C2 | semidirect |
| 5. C2×#10587495 | C2 | semidirect |
| 23. C2×Dic68 | C22 | semidirect |
| 24. #10587495 | C22 | semidirect |
| 25. #10587490 | C22 | semidirect |
| 108. C2×C17 | #473 | semidirect |
| 129. C17 | C2×#473 | semidirect |
| 205. C2 | #11763084 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587637 | 2 |
| C22×Dic68 | 2 |
| #11763084 | 2 |
| C2×#10587490 | 2 |
| C2×#10587495 | 2 |
| C2×C17×#131 | 2 |
| C2×#473 | 17 |