Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
380 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 380 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 |
|---|---|---|
| 1. #11763341 | C2 | semidirect |
| 2. #11763210 | C2 | semidirect |
| 3. #11763192 | C2 | semidirect |
| 4. #11763162 | C2 | semidirect |
| 5. #11763051 | C2 | semidirect |
| 7. #11763037 | C2 | semidirect |
| 8. C4×Dic68 | C2 | semidirect |
| 9. C4×#63229 | C2 | semidirect |
| 10. C4×C8×D17 | C2 | semidirect |
| 11. C4×D8×C17 | C2 | semidirect |
| 123. C4×D8 | D17 | semidirect |
| 157. C17 | #3168 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763341 | 2 |
| #11763210 | 2 |
| #11763192 | 2 |
| #11763162 | 2 |
| #11763051 | 2 |
| #11763042 | 2 |
| #11763037 | 2 |
| C4×Dic68 | 2 |
| C4×#63229 | 2 |
| C4×C8×D17 | 2 |
| C4×D8×C17 | 2 |
| #3168 | 17 |