Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
348 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 103 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. C2×#10587479 | C2 | semidirect |
| 3. C2×#10587487 | C2 | semidirect |
| 4. C2×C8×Dic17 | C2 | semidirect |
| 5. #11762714 | C2 | semidirect |
| 15. C2×#63229 | C4 | semidirect |
| 81. C2×Dic17 | SD16 | semidirect |
| 87. #3622 | C22⋊C4 | semidirect |
| 136. C17 | #1968 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#63229 | 2 |
| C2×#10587479 | 2 |
| C2×#10587487 | 2 |
| C2×C8×Dic17 | 2 |
| #11762714 | 2 |
| #11762712 | 2 |
| C2×C17×#102 | 2 |
| #1968 | 17 |