Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
384 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 123 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×#559 | C2 | semidirect |
| 2. #11719290 | C2 | semidirect |
| 3. #11718736 | C2 | semidirect |
| 5. #11718720 | C2 | semidirect |
| 6. #11718718 | C2 | semidirect |
| 7. C4×#6107 | C2 | semidirect |
| 8. #11718688 | C2 | semidirect |
| 9. Q8×#1055 | C2 | semidirect |
| 10. #11718677 | C2 | semidirect |
| 11. C4×#6104 | C2 | semidirect |
| 107. #559 | D13 | semidirect |
| 203. C13 | #3396 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#559 | 2 |
| #11719290 | 2 |
| #11718736 | 2 |
| #11718734 | 2 |
| #11718720 | 2 |
| #11718718 | 2 |
| C4×#6107 | 2 |
| #11718688 | 2 |
| Q8×#1055 | 2 |
| #11718677 | 2 |
| C4×#6104 | 2 |
| #3396 | 13 |