Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
342 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 342 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 |
|---|---|---|
| 3. #11763153 | C2 | semidirect |
| 4. #11763141 | C2 | semidirect |
| 5. #11763101 | C2 | semidirect |
| 6. #11763091 | C2 | semidirect |
| 7. #11763068 | C2 | semidirect |
| 8. C4×Dic68 | C2 | semidirect |
| 10. #11762848 | C2 | semidirect |
| 11. C17×#498 | C2 | semidirect |
| 115. #498 | D17 | semidirect |
| 157. C17 | #3356 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763533 | 2 |
| #11763520 | 2 |
| #11763153 | 2 |
| #11763141 | 2 |
| #11763101 | 2 |
| #11763091 | 2 |
| #11763068 | 2 |
| C4×Dic68 | 2 |
| #11762888 | 2 |
| #11762848 | 2 |
| C17×#498 | 2 |
| #3356 | 17 |