Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
552 conjugacy classes of subgroups; only the 185 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 185 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. #11762703 | C2 | semidirect |
| 3. #11762703 | C2 | semidirect |
| 4. #11762690 | C2 | semidirect |
| 6. C4×#63225 | C2 | semidirect |
| 7. C22⋊C4×Dic17 | C2 | semidirect |
| 8. C22⋊C4×Dic17 | C2 | semidirect |
| 21. #10587621 | C4 | semidirect |
| 44. C22×Dic17 | C2×C4 | semidirect |
| 56. C22⋊Dic17 | C2×C4 | semidirect |
| 58. #63225 | C2×C4 | semidirect |
| 158. C17 | #2374 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587621 | 2 |
| #11762703 | 2 |
| #11762690 | 2 |
| #11762689 | 2 |
| C4×#63225 | 2 |
| C22⋊C4×Dic17 | 2 |
| C17×#390 | 2 |
| #2374 | 17 |