Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
524 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 524 conjugacy classes of subgroups — too many to draw. Only its 133 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. #11719510 | C2 | semidirect |
| 2. C22×#6104 | C2 | semidirect |
| 3. C2×#88161 | C2 | semidirect |
| 4. #11719230 | C2 | semidirect |
| 5. C13×#418 | C2 | semidirect |
| 6. #11718792 | C2 | semidirect |
| 7. #11718659 | C2 | semidirect |
| 8. #11718443 | C2 | semidirect |
| 9. #11718436 | C2 | semidirect |
| 17. #88192 | C22 | semidirect |
| 25. C2×#6094 | C22 | semidirect |
| 26. C2×C8×D13 | C22 | semidirect |
| 27. #88149 | C22 | semidirect |
| 31. C13×#102 | C22 | semidirect |
| 32. #88061 | C22 | semidirect |
| 33. #88048 | C22 | semidirect |
| 34. #88047 | C22 | semidirect |
| 66. C2×#1055 | D4 | semidirect |
| 111. #418 | D13 | semidirect |
| 153. #102 | C2×D13 | semidirect |
| 196. C13 | #3058 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719510 | 2 |
| C22×#6104 | 2 |
| C2×#88161 | 2 |
| #11719230 | 2 |
| C13×#418 | 2 |
| #11718792 | 2 |
| #11718659 | 2 |
| #11718443 | 2 |
| #11718436 | 2 |
| #3058 | 13 |