Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
238 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 73 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. #11762655 | C2 | semidirect |
| 3. #11762547 | C2 | semidirect |
| 5. C17×#431 | C2 | semidirect |
| 13. #10587561 | C4 | semidirect |
| 14. C4×D68 | C4 | semidirect |
| 16. #10587556 | C4 | semidirect |
| 17. C4×Dic34 | C4 | semidirect |
| 90. #431 | D17 | semidirect |
| 116. C17 | #1500 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763343 | 2 |
| #11762655 | 2 |
| #11762547 | 2 |
| #11762544 | 2 |
| C17×#431 | 2 |
| #1500 | 17 |