Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
360 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 99 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×#10587487 | C2 | semidirect |
| 4. C2×#10587481 | C2 | semidirect |
| 6. #11762571 | C2 | semidirect |
| 7. C17×#340 | C2 | semidirect |
| 22. #10587583 | C4 | semidirect |
| 130. #340 | D17 | semidirect |
| 157. C17 | #1894 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#63218 | 2 |
| C2×#10587583 | 2 |
| C2×#10587487 | 2 |
| C2×#10587481 | 2 |
| #11762666 | 2 |
| #11762571 | 2 |
| C17×#340 | 2 |
| #1894 | 17 |