Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
484 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 125 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. #11719433 | C2 | semidirect |
| 3. C13×#486 | C2 | semidirect |
| 4. #11718749 | C2 | semidirect |
| 5. #11718731 | C2 | semidirect |
| 6. #11718431 | C2 | semidirect |
| 7. #11718425 | C2 | semidirect |
| 8. #11718355 | C2 | semidirect |
| 9. C4×#6094 | C2 | semidirect |
| 13. C13×C4⋊Q8 | C22 | semidirect |
| 23. #88144 | C22 | semidirect |
| 27. #88123 | C22 | semidirect |
| 28. C13×#102 | C22 | semidirect |
| 29. C4×C8×C13 | C22 | semidirect |
| 30. #88072 | C22 | semidirect |
| 31. #88061 | C22 | semidirect |
| 32. #88055 | C22 | semidirect |
| 33. #88049 | C22 | semidirect |
| 34. C4×#1055 | C22 | semidirect |
| 105. #486 | D13 | semidirect |
| 132. C4⋊Q8 | C2×D13 | semidirect |
| 148. #102 | C2×D13 | semidirect |
| 151. C4×C8 | C2×D13 | semidirect |
| 191. C13 | #3138 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719433 | 2 |
| D13×#127 | 2 |
| C13×#486 | 2 |
| #11718749 | 2 |
| #11718731 | 2 |
| #11718431 | 2 |
| #11718425 | 2 |
| #11718355 | 2 |
| C4×#6094 | 2 |
| #3138 | 13 |