Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
488 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 141 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. #11718749 | C2 | semidirect |
| 4. #11718746 | C2 | semidirect |
| 5. #11718707 | C2 | semidirect |
| 6. #11718688 | C2 | semidirect |
| 7. #11718586 | C2 | semidirect |
| 11. C13×C4⋊Q8 | C22 | semidirect |
| 12. C13×C4⋊Q8 | C22 | semidirect |
| 17. C4×Q8×C13 | C22 | semidirect |
| 20. C2×#6106 | C22 | semidirect |
| 26. #88049 | C22 | semidirect |
| 27. C4⋊#1055 | C22 | semidirect |
| 28. C4×#1055 | C22 | semidirect |
| 70. C2×C4×C13 | SD16 | semidirect |
| 84. #533 | D13 | semidirect |
| 111. C4⋊Q8 | C2×D13 | semidirect |
| 112. C4⋊Q8 | C2×D13 | semidirect |
| 121. C4×Q8 | C2×D13 | semidirect |
| 162. C13 | #3208 | semidirect |
| 180. C2×C4 | #6106 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#533 | 2 |
| C2×#88128 | 2 |
| #11718749 | 2 |
| #11718746 | 2 |
| #11718707 | 2 |
| #11718688 | 2 |
| #11718586 | 2 |
| #3208 | 13 |