Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
366 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 366 conjugacy classes of subgroups — too many to draw. Only its 121 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. #11763219 | C2 | semidirect |
| 3. #11763175 | C2 | semidirect |
| 4. #11763133 | C2 | semidirect |
| 5. #11763096 | C2 | semidirect |
| 6. #11763086 | C2 | semidirect |
| 7. #11762866 | C2 | semidirect |
| 8. C17×#533 | C2 | semidirect |
| 102. #533 | D17 | semidirect |
| 139. C17 | #3235 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763359 | 2 |
| #11763219 | 2 |
| #11763175 | 2 |
| #11763133 | 2 |
| #11763096 | 2 |
| #11763086 | 2 |
| #11762866 | 2 |
| C17×#533 | 2 |
| #3235 | 17 |