Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
484 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 127 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. C2×#10587598 | C2 | semidirect |
| 2. C2×#10587587 | C2 | semidirect |
| 3. #11763388 | C2 | semidirect |
| 4. #11763054 | C2 | semidirect |
| 5. #11763053 | C2 | semidirect |
| 6. #11763051 | C2 | semidirect |
| 7. #11763050 | C2 | semidirect |
| 8. #11763042 | C2 | semidirect |
| 9. #107×D17 | C2 | semidirect |
| 10. #11762807 | C2 | semidirect |
| 11. C17×#466 | C2 | semidirect |
| 80. C8×D17 | D4 | semidirect |
| 145. #466 | D17 | semidirect |
| 184. C17 | #3061 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587598 | 2 |
| C2×#10587587 | 2 |
| #11763388 | 2 |
| #11763054 | 2 |
| #11763053 | 2 |
| #11763051 | 2 |
| #11763050 | 2 |
| #11763042 | 2 |
| #107×D17 | 2 |
| #11762807 | 2 |
| C17×#466 | 2 |
| #3061 | 17 |