Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
490 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 149 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×#519 | C2 | semidirect |
| 2. C2×#88196 | C2 | semidirect |
| 3. C22×#6106 | C2 | semidirect |
| 5. #11718689 | C2 | semidirect |
| 6. #11718688 | C2 | semidirect |
| 7. #11718663 | C2 | semidirect |
| 8. #11718662 | C2 | semidirect |
| 9. #11718660 | C2 | semidirect |
| 14. C4×Q8×C13 | C22 | semidirect |
| 18. C2×#6107 | C22 | semidirect |
| 22. C2×#6106 | C22 | semidirect |
| 29. #88050 | C22 | semidirect |
| 31. #88049 | C22 | semidirect |
| 32. C4⋊#1055 | C22 | semidirect |
| 36. C2×Q8×C13 | D4 | semidirect |
| 100. #519 | D13 | semidirect |
| 136. C4×Q8 | C2×D13 | semidirect |
| 155. C2×Q8 | D52 | semidirect |
| 183. C13 | #3043 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#519 | 2 |
| C2×#88196 | 2 |
| C22×#6106 | 2 |
| #11719230 | 2 |
| #11718689 | 2 |
| #11718688 | 2 |
| #11718663 | 2 |
| #11718662 | 2 |
| #11718660 | 2 |
| #3043 | 13 |