Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
400 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 400 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. #11763359 | C2 | semidirect |
| 2. #11763191 | C2 | semidirect |
| 3. #11763166 | C2 | semidirect |
| 4. #11763019 | C2 | semidirect |
| 5. #11763014 | C2 | semidirect |
| 6. #11763009 | C2 | semidirect |
| 7. #11763004 | C2 | semidirect |
| 8. #11762969 | C2 | semidirect |
| 9. #11762952 | C2 | semidirect |
| 10. #11762862 | C2 | semidirect |
| 11. C17×#529 | C2 | semidirect |
| 140. #529 | D17 | semidirect |
| 187. C17 | #3212 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763359 | 2 |
| #11763191 | 2 |
| #11763166 | 2 |
| #11763019 | 2 |
| #11763014 | 2 |
| #11763009 | 2 |
| #11763004 | 2 |
| #11762969 | 2 |
| #11762952 | 2 |
| #11762862 | 2 |
| C17×#529 | 2 |
| #3212 | 17 |