Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
222 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 222 conjugacy classes of subgroups — too many to draw. Only its 75 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. #11762836 | C2 | semidirect |
| 5. C2×#10587474 | C2 | semidirect |
| 6. #11762573 | C2 | semidirect |
| 7. C17×#339 | C2 | semidirect |
| 16. #10587481 | C4 | semidirect |
| 17. #10587480 | C4 | semidirect |
| 92. #339 | D17 | semidirect |
| 111. C17 | #1938 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11762836 | 2 |
| C2×#10587476 | 2 |
| #11762803 | 2 |
| #11762777 | 2 |
| C2×#10587474 | 2 |
| #11762573 | 2 |
| C17×#339 | 2 |
| #1938 | 17 |