Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
256 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 72 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×#10587535 | C2 | semidirect |
| 2. #11763819 | C2 | semidirect |
| 4. #11763692 | C2 | semidirect |
| 9. C17×#131 | C4 | semidirect |
| 10. #10587634 | C4 | semidirect |
| 12. #10587593 | C4 | semidirect |
| 16. #10587587 | C4 | semidirect |
| 123. #131 | #595 | semidirect |
| 136. C17 | #1814 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587535 | 2 |
| #11763819 | 2 |
| #11763806 | 2 |
| #11763692 | 2 |
| #131×D17 | 2 |
| #1814 | 17 |