Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
1460 conjugacy classes of subgroups; only the 754 normal subgroups are shown.
This group has 1460 conjugacy classes of subgroups — too many to draw. Only its 754 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. #11763889 | C2 | direct (N × H) |
| 2. C2×#10587680 | C2 | semidirect |
| 3. C2×D17⋊M16 | C2 | semidirect |
| 13. #10587680 | C22 | semidirect |
| 14. D17⋊M16 | C22 | semidirect |
| 15. C2×#63243 | C22 | semidirect |
| 16. C2×#63242 | C22 | semidirect |
| 33. #63243 | C23 | semidirect |
| 34. #63242 | C23 | semidirect |
| 67. C2×C17 | #568 | semidirect |
| 82. C17 | C2×#568 | semidirect |
| 129. C2 | #11763889 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763889 | 2 |
| C2×#10587680 | 2 |
| C2×D17⋊M16 | 2 |
| C22×#63256 | 2 |
| C2×#568 | 17 |