Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
340 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 68 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×#10587543 | C2 | semidirect |
| 2. #11763751 | C2 | semidirect |
| 3. #11763661 | C2 | semidirect |
| 4. #11763660 | C2 | semidirect |
| 7. C2×D4×D17 | C4 | semidirect |
| 12. C17×#121 | C4 | semidirect |
| 15. #10587616 | C4 | semidirect |
| 17. C4⋊C4×D17 | C4 | semidirect |
| 20. (C2×#595)⋊C4 | C22 | semidirect |
| 22. #10587543 | C22 | semidirect |
| 144. #121 | #595 | semidirect |
| 152. C17 | #1519 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587543 | 2 |
| #11763751 | 2 |
| #11763661 | 2 |
| #11763660 | 2 |
| #121×D17 | 2 |
| #1519 | 17 |