Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
568 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 153 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. #11762724 | C2 | semidirect |
| 3. #11762710 | C2 | semidirect |
| 4. #11762710 | C2 | semidirect |
| 5. #11762700 | C2 | semidirect |
| 6. #11762678 | C2 | semidirect |
| 7. #11762674 | C2 | semidirect |
| 8. C4×C22⋊Dic17 | C2 | semidirect |
| 9. C2×C17×#117 | C2 | semidirect |
| 114. C2×#117 | D17 | semidirect |
| 148. C17 | #2500 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587616 | 2 |
| #11762724 | 2 |
| #11762710 | 2 |
| #11762700 | 2 |
| #11762678 | 2 |
| #11762674 | 2 |
| C4×C22⋊Dic17 | 2 |
| C2×C17×#117 | 2 |
| #2500 | 17 |