Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
228 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 64 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×#10587529 | C2 | semidirect |
| 2. #11763819 | C2 | semidirect |
| 3. #11763722 | C2 | semidirect |
| 4. #11763721 | C2 | semidirect |
| 8. C17×#135 | C4 | semidirect |
| 10. #10587605 | C4 | semidirect |
| 14. #10587598 | C4 | semidirect |
| 16. #10587590 | C4 | semidirect |
| 114. #135 | #595 | semidirect |
| 125. C17 | #2138 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587529 | 2 |
| #11763819 | 2 |
| #11763722 | 2 |
| #11763721 | 2 |
| #135×D17 | 2 |
| #2138 | 17 |