Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
400 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 121 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×#533 | C2 | semidirect |
| 3. #11718750 | C2 | semidirect |
| 4. #11718747 | C2 | semidirect |
| 5. #11718711 | C2 | semidirect |
| 7. #11718689 | C2 | semidirect |
| 8. #11718587 | C2 | semidirect |
| 11. C13×C4⋊Q8 | C22 | semidirect |
| 12. C13×C4⋊Q8 | C22 | semidirect |
| 17. C4×Q8×C13 | C22 | semidirect |
| 20. C2×#6107 | C22 | semidirect |
| 29. #88050 | C22 | semidirect |
| 31. C4⋊#1055 | C22 | semidirect |
| 32. #88043 | C22 | semidirect |
| 91. #533 | D13 | semidirect |
| 120. C4⋊Q8 | C2×D13 | semidirect |
| 121. C4⋊Q8 | C2×D13 | semidirect |
| 130. C4×Q8 | C2×D13 | semidirect |
| 177. C13 | #3215 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#533 | 2 |
| C2×#88129 | 2 |
| #11718750 | 2 |
| #11718747 | 2 |
| #11718711 | 2 |
| #11718707 | 2 |
| #11718689 | 2 |
| #11718587 | 2 |
| #3215 | 13 |