Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
398 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 115 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. #11763520 | C2 | semidirect |
| 3. #11763121 | C2 | semidirect |
| 4. #11763101 | C2 | semidirect |
| 5. #11763054 | C2 | semidirect |
| 6. #11763006 | C2 | semidirect |
| 7. #11762972 | C2 | semidirect |
| 8. C4×Dic68 | C2 | semidirect |
| 9. #11762888 | C2 | semidirect |
| 10. #11762807 | C2 | semidirect |
| 11. C17×#486 | C2 | semidirect |
| 126. #486 | D17 | semidirect |
| 169. C17 | #3333 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763520 | 2 |
| #11763479 | 2 |
| #11763121 | 2 |
| #11763101 | 2 |
| #11763054 | 2 |
| #11763006 | 2 |
| #11762972 | 2 |
| C4×Dic68 | 2 |
| #11762888 | 2 |
| #11762807 | 2 |
| C17×#486 | 2 |
| #3333 | 17 |