Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
326 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 87 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 |
|---|---|---|
| 1. C2×#10587574 | C2 | semidirect |
| 5. #11762571 | C2 | semidirect |
| 6. #11762563 | C2 | semidirect |
| 7. C17×#340 | C2 | semidirect |
| 35. C2×D68 | Q8 | semidirect |
| 121. #340 | D17 | semidirect |
| 146. C17 | #2023 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587574 | 2 |
| C2×#10587492 | 2 |
| C2×#10587480 | 2 |
| #11762710 | 2 |
| #11762571 | 2 |
| #11762563 | 2 |
| C17×#340 | 2 |
| #2023 | 17 |