Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
482 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 482 conjugacy classes of subgroups — too many to draw. Only its 125 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×#10587598 | C2 | semidirect |
| 2. C22×Dic68 | C2 | semidirect |
| 3. #11763465 | C2 | semidirect |
| 4. #11763192 | C2 | semidirect |
| 5. #11763051 | C2 | semidirect |
| 6. #11763030 | C2 | semidirect |
| 7. #11762972 | C2 | semidirect |
| 8. #11762947 | C2 | semidirect |
| 9. #11762903 | C2 | semidirect |
| 10. C8×C22⋊D17 | C2 | semidirect |
| 11. C17×#466 | C2 | semidirect |
| 78. Dic68 | D4 | semidirect |
| 117. C22×C17 | #135 | semidirect |
| 136. #466 | D17 | semidirect |
| 177. C17 | #3285 | semidirect |
| 256. C22 | #10587598 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587598 | 2 |
| C22×Dic68 | 2 |
| #11763465 | 2 |
| #11763192 | 2 |
| #11763051 | 2 |
| #11763030 | 2 |
| #11762972 | 2 |
| #11762947 | 2 |
| #11762903 | 2 |
| C8×C22⋊D17 | 2 |
| C17×#466 | 2 |
| #3285 | 17 |