Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
300 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 90 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 |
|---|---|---|
| 3. #11763774 | C2 | semidirect |
| 4. C2×C8×#595 | C2 | semidirect |
| 5. #11763685 | C2 | semidirect |
| 6. #11763679 | C2 | semidirect |
| 10. #10587680 | C4 | semidirect |
| 19. #10587550 | C4 | semidirect |
| 23. C17×#103 | C4 | semidirect |
| 24. #10587506 | C4 | semidirect |
| 25. #10587492 | C4 | semidirect |
| 26. #10587480 | C4 | semidirect |
| 130. #103 | #595 | semidirect |
| 136. C17 | #1764 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587680 | 2 |
| C2×#10587550 | 2 |
| #11763774 | 2 |
| C2×C8×#595 | 2 |
| #11763685 | 2 |
| #11763679 | 2 |
| #11762804 | 2 |
| #1764 | 17 |