Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
386 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 115 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. #11763105 | C2 | semidirect |
| 4. #11763104 | C2 | semidirect |
| 5. #11763087 | C2 | semidirect |
| 6. #11763054 | C2 | semidirect |
| 7. #11763052 | C2 | semidirect |
| 8. #11763012 | C2 | semidirect |
| 9. #11763006 | C2 | semidirect |
| 10. #11762831 | C2 | semidirect |
| 11. C17×#460 | C2 | semidirect |
| 142. #460 | D17 | semidirect |
| 180. C17 | #3254 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763363 | 2 |
| #11763357 | 2 |
| #11763105 | 2 |
| #11763104 | 2 |
| #11763087 | 2 |
| #11763054 | 2 |
| #11763052 | 2 |
| #11763012 | 2 |
| #11763006 | 2 |
| #11762831 | 2 |
| C17×#460 | 2 |
| #3254 | 17 |