Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
390 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 390 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 |
|---|---|---|
| 1. #11763363 | C2 | semidirect |
| 3. #11763202 | C2 | semidirect |
| 4. #11763170 | C2 | semidirect |
| 5. #11763016 | C2 | semidirect |
| 6. #11763010 | C2 | semidirect |
| 7. #11763009 | C2 | semidirect |
| 8. #11762974 | C2 | semidirect |
| 9. #11762970 | C2 | semidirect |
| 10. #11762865 | C2 | semidirect |
| 11. C17×#462 | C2 | semidirect |
| 141. #462 | D17 | semidirect |
| 183. C17 | #3216 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763363 | 2 |
| #11763360 | 2 |
| #11763202 | 2 |
| #11763170 | 2 |
| #11763016 | 2 |
| #11763010 | 2 |
| #11763009 | 2 |
| #11762974 | 2 |
| #11762970 | 2 |
| #11762865 | 2 |
| C17×#462 | 2 |
| #3216 | 17 |