Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
222 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 222 conjugacy classes of subgroups — too many to draw. Only its 60 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. #11763816 | C2 | semidirect |
| 4. C2×#10587532 | C2 | semidirect |
| 5. #11763685 | C2 | semidirect |
| 6. #11763679 | C2 | semidirect |
| 21. C17×#102 | C4 | semidirect |
| 22. #10587503 | C4 | semidirect |
| 23. #10587487 | C4 | semidirect |
| 24. #10587481 | C4 | semidirect |
| 126. #102 | #595 | semidirect |
| 130. C17 | #1938 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763816 | 2 |
| C2×#10587548 | 2 |
| #11763783 | 2 |
| C2×#10587532 | 2 |
| #11763685 | 2 |
| #11763679 | 2 |
| #11762802 | 2 |
| #1938 | 17 |