Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
524 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 524 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×#535 | C2 | semidirect |
| 2. #11719535 | C2 | semidirect |
| 3. C2×#88202 | C2 | semidirect |
| 4. C22×#6104 | C2 | semidirect |
| 5. #11718876 | C2 | semidirect |
| 6. #11718700 | C2 | semidirect |
| 7. #11718699 | C2 | semidirect |
| 8. #11718662 | C2 | semidirect |
| 9. #11718659 | C2 | semidirect |
| 15. C13×#121 | C22 | semidirect |
| 25. #88184 | C22 | semidirect |
| 28. C2×#6099 | C22 | semidirect |
| 30. C22×#1055 | C22 | semidirect |
| 31. #88072 | C22 | semidirect |
| 32. #88049 | C22 | semidirect |
| 33. #88048 | C22 | semidirect |
| 34. #88047 | C22 | semidirect |
| 67. C2×#1055 | D4 | semidirect |
| 106. #535 | D13 | semidirect |
| 145. #121 | 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 |
|---|---|
| C13×#535 | 2 |
| #11719535 | 2 |
| C2×#88202 | 2 |
| C22×#6104 | 2 |
| #11718876 | 2 |
| #11718700 | 2 |
| #11718699 | 2 |
| #11718662 | 2 |
| #11718659 | 2 |
| #3058 | 13 |