Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
338 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 3. #11763208 | C2 | semidirect |
| 4. #11763188 | C2 | semidirect |
| 5. #11763178 | C2 | semidirect |
| 8. #11762913 | C2 | semidirect |
| 9. #11762901 | C2 | semidirect |
| 11. C17×#491 | C2 | semidirect |
| 105. #491 | D17 | semidirect |
| 141. C17 | #3177 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763422 | 2 |
| #11763420 | 2 |
| #11763208 | 2 |
| #11763188 | 2 |
| #11763178 | 2 |
| #11763066 | 2 |
| #11763049 | 2 |
| #11762913 | 2 |
| #11762901 | 2 |
| #11762766 | 2 |
| C17×#491 | 2 |
| #3177 | 17 |