Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
418 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 418 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×#550 | C2 | semidirect |
| 2. #11719290 | C2 | semidirect |
| 3. #11718736 | C2 | semidirect |
| 4. #11718735 | C2 | semidirect |
| 5. #11718734 | C2 | semidirect |
| 6. #11718733 | C2 | semidirect |
| 7. #11718685 | C2 | semidirect |
| 8. C4×#6105 | C2 | semidirect |
| 9. #11718677 | C2 | semidirect |
| 10. #11718676 | C2 | semidirect |
| 11. #11718675 | C2 | semidirect |
| 109. #1055 | #41 | semidirect |
| 111. #550 | D13 | semidirect |
| 211. C13 | #3399 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#550 | 2 |
| #11719290 | 2 |
| #11718736 | 2 |
| #11718735 | 2 |
| #11718734 | 2 |
| #11718733 | 2 |
| #11718685 | 2 |
| C4×#6105 | 2 |
| #11718677 | 2 |
| #11718676 | 2 |
| #11718675 | 2 |
| #3399 | 13 |