Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
406 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 406 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×#556 | C2 | semidirect |
| 2. #11719282 | C2 | semidirect |
| 3. #11718746 | C2 | semidirect |
| 4. #11718744 | C2 | semidirect |
| 5. #11718719 | C2 | semidirect |
| 6. #11718718 | C2 | semidirect |
| 7. #11718688 | C2 | semidirect |
| 8. #11718687 | C2 | semidirect |
| 9. #11718685 | C2 | semidirect |
| 10. #11718676 | C2 | semidirect |
| 11. C4×#6104 | C2 | semidirect |
| 107. #1055 | #41 | semidirect |
| 108. #556 | D13 | semidirect |
| 209. C13 | #3397 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#556 | 2 |
| #11719282 | 2 |
| #11718746 | 2 |
| #11718744 | 2 |
| #11718719 | 2 |
| #11718718 | 2 |
| #11718688 | 2 |
| #11718687 | 2 |
| #11718685 | 2 |
| #11718676 | 2 |
| C4×#6104 | 2 |
| #3397 | 13 |