Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
704 conjugacy classes of subgroups; only the 169 normal subgroups are shown.
This group has 704 conjugacy classes of subgroups — too many to draw. Only its 169 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×#10587561 | C2 | semidirect |
| 3. C2×#10587622 | C2 | semidirect |
| 4. #11762725 | C2 | semidirect |
| 5. #11762714 | C2 | semidirect |
| 6. #11762710 | C2 | semidirect |
| 7. #11762688 | C2 | semidirect |
| 8. C4×C4⋊Dic17 | C2 | semidirect |
| 9. C2×C4×D4×C17 | C2 | semidirect |
| 56. C42×C17 | D4 | semidirect |
| 124. C2×C4×D4 | D17 | semidirect |
| 158. C17 | #2544 | semidirect |
| 191. C42 | C22⋊D17 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587626 | 2 |
| C2×#10587561 | 2 |
| C2×#10587622 | 2 |
| #11762725 | 2 |
| #11762714 | 2 |
| #11762710 | 2 |
| #11762688 | 2 |
| C4×C4⋊Dic17 | 2 |
| C2×C4×D4×C17 | 2 |
| #2544 | 17 |