Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
314 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 79 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 |
|---|---|---|
| 2. #11763286 | C2 | semidirect |
| 4. C2×#10587495 | C2 | semidirect |
| 5. #11762566 | C2 | semidirect |
| 6. #11762565 | C2 | semidirect |
| 12. #10587630 | C4 | semidirect |
| 13. #10587622 | C4 | semidirect |
| 134. C17 | #1912 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763380 | 2 |
| #11763286 | 2 |
| #11762826 | 2 |
| C2×#10587495 | 2 |
| #11762566 | 2 |
| #11762565 | 2 |
| C17×#421 | 2 |
| #1912 | 17 |