Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
348 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 125 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. C13×#557 | C2 | semidirect |
| 3. #11718755 | C2 | semidirect |
| 5. #11718729 | C2 | semidirect |
| 6. #11718727 | C2 | semidirect |
| 7. C4×#6107 | C2 | semidirect |
| 8. #11718689 | C2 | semidirect |
| 10. C4×#6106 | C2 | semidirect |
| 11. Q8×#1055 | C2 | semidirect |
| 100. #557 | D13 | semidirect |
| 190. C13 | #3365 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#557 | 2 |
| #11719290 | 2 |
| #11718755 | 2 |
| #11718749 | 2 |
| #11718729 | 2 |
| #11718727 | 2 |
| C4×#6107 | 2 |
| #11718689 | 2 |
| #11718688 | 2 |
| C4×#6106 | 2 |
| Q8×#1055 | 2 |
| #3365 | 13 |