Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
386 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 117 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. C2×#10587573 | C2 | semidirect |
| 4. #11763115 | C2 | semidirect |
| 5. #11763034 | C2 | semidirect |
| 6. #11762964 | C2 | semidirect |
| 8. #11762913 | C2 | semidirect |
| 9. #11762908 | C2 | semidirect |
| 10. #11762863 | C2 | semidirect |
| 11. C17×#484 | C2 | semidirect |
| 129. #484 | D17 | semidirect |
| 174. C17 | #3117 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763345 | 2 |
| C2×#10587573 | 2 |
| #11763127 | 2 |
| #11763115 | 2 |
| #11763034 | 2 |
| #11762964 | 2 |
| #11762950 | 2 |
| #11762913 | 2 |
| #11762908 | 2 |
| #11762863 | 2 |
| C17×#484 | 2 |
| #3117 | 17 |