Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
368 conjugacy classes of subgroups; only the 200 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 200 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. #11719162 | C2 | semidirect |
| 3. #11719096 | C2 | semidirect |
| 4. D13⋊M32 | C2 | semidirect |
| 5. C2×D13⋊C16 | C2 | semidirect |
| 13. #88106 | C22 | semidirect |
| 14. C2×#6092 | C22 | semidirect |
| 15. #88098 | C22 | semidirect |
| 18. D13⋊C16 | C22 | semidirect |
| 83. D13 | #504 | semidirect |
| 102. C13 | C2×#504 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D13×#131 | 2 |
| #11719162 | 2 |
| #11719096 | 2 |
| D13⋊M32 | 2 |
| C2×D13⋊C16 | 2 |
| C2×#504 | 13 |