Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
440 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 145 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. #11718748 | C2 | semidirect |
| 4. #11718745 | C2 | semidirect |
| 5. #11718727 | C2 | semidirect |
| 7. #11718656 | C2 | semidirect |
| 8. #11718585 | C2 | semidirect |
| 11. C13×C4⋊Q8 | C22 | semidirect |
| 12. C13×C4⋊Q8 | C22 | semidirect |
| 13. C13×#125 | C22 | semidirect |
| 29. #88048 | C22 | semidirect |
| 30. #88047 | C22 | semidirect |
| 31. C4⋊#1055 | C22 | semidirect |
| 32. C4⋊#1055 | C22 | semidirect |
| 42. C2×D52 | Q8 | semidirect |
| 93. #533 | D13 | semidirect |
| 122. C4⋊Q8 | C2×D13 | semidirect |
| 123. C4⋊Q8 | C2×D13 | semidirect |
| 124. #125 | C2×D13 | semidirect |
| 180. C13 | #3077 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#533 | 2 |
| C2×C4×D52 | 2 |
| #11718748 | 2 |
| #11718745 | 2 |
| #11718727 | 2 |
| #11718662 | 2 |
| #11718656 | 2 |
| #11718585 | 2 |
| #3077 | 13 |