Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
284 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 91 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 |
|---|---|---|
| 3. C2×#10587486 | C2 | semidirect |
| 5. #11762708 | C2 | semidirect |
| 6. #11762571 | C2 | semidirect |
| 7. C17×#340 | C2 | semidirect |
| 21. #10587480 | C4 | semidirect |
| 117. #340 | D17 | semidirect |
| 140. C17 | #1936 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587492 | 2 |
| C2×#10587480 | 2 |
| C2×#10587486 | 2 |
| #11762710 | 2 |
| #11762708 | 2 |
| #11762571 | 2 |
| C17×#340 | 2 |
| #1936 | 17 |