Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
676 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 676 conjugacy classes of subgroups — too many to draw. Only its 165 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×#10587633 | C2 | semidirect |
| 3. C2×Q8×Dic17 | C2 | semidirect |
| 4. #11762725 | C2 | semidirect |
| 5. #11762712 | C2 | semidirect |
| 6. #11762711 | C2 | semidirect |
| 7. #11762709 | C2 | semidirect |
| 8. C4×#63225 | C2 | semidirect |
| 9. C2×C17×#124 | C2 | semidirect |
| 35. C2×Q8×C17 | D4 | semidirect |
| 120. Dic17 | #124 | semidirect |
| 123. C2×#124 | D17 | semidirect |
| 158. C17 | #2548 | semidirect |
| 163. C2×Q8 | 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×#10587633 | 2 |
| C2×Q8×Dic17 | 2 |
| #11762725 | 2 |
| #11762712 | 2 |
| #11762711 | 2 |
| #11762709 | 2 |
| C4×#63225 | 2 |
| C2×C17×#124 | 2 |
| #2548 | 17 |