Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
354 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 125 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. #11763516 | C2 | semidirect |
| 3. #11763214 | C2 | semidirect |
| 4. #11763151 | C2 | semidirect |
| 5. #11763123 | C2 | semidirect |
| 6. #11763105 | C2 | semidirect |
| 7. #11763100 | C2 | semidirect |
| 8. #11763055 | C2 | semidirect |
| 9. C4×#63219 | C2 | semidirect |
| 10. #11762851 | C2 | semidirect |
| 11. C17×#436 | C2 | semidirect |
| 126. #436 | D17 | semidirect |
| 162. C17 | #3357 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763524 | 2 |
| #11763516 | 2 |
| #11763214 | 2 |
| #11763151 | 2 |
| #11763123 | 2 |
| #11763105 | 2 |
| #11763100 | 2 |
| #11763055 | 2 |
| C4×#63219 | 2 |
| #11762851 | 2 |
| C17×#436 | 2 |
| #3357 | 17 |