Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
388 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 117 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×#540 | C2 | semidirect |
| 2. #11719231 | C2 | semidirect |
| 3. #11718737 | C2 | semidirect |
| 4. #11718735 | C2 | semidirect |
| 5. #11718730 | C2 | semidirect |
| 6. #11718729 | C2 | semidirect |
| 7. #11718701 | C2 | semidirect |
| 8. #11718698 | C2 | semidirect |
| 9. #11718680 | C2 | semidirect |
| 10. #11718677 | C2 | semidirect |
| 11. #11718661 | C2 | semidirect |
| 100. #540 | D13 | semidirect |
| 192. C13 | #3221 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#540 | 2 |
| #11719231 | 2 |
| #11718737 | 2 |
| #11718735 | 2 |
| #11718730 | 2 |
| #11718729 | 2 |
| #11718701 | 2 |
| #11718698 | 2 |
| #11718680 | 2 |
| #11718677 | 2 |
| #11718661 | 2 |
| #3221 | 13 |