Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
528 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 189 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×#518 | C2 | semidirect |
| 3. #11719226 | C2 | semidirect |
| 4. #11718876 | C2 | semidirect |
| 5. #11718675 | C2 | semidirect |
| 6. C4×#6104 | C2 | semidirect |
| 7. #11718662 | C2 | semidirect |
| 8. #11718659 | C2 | semidirect |
| 9. #11718658 | C2 | semidirect |
| 13. C4×D4×C13 | C22 | semidirect |
| 17. C2×#6104 | C4 | semidirect |
| 25. C4×D52 | C22 | semidirect |
| 26. #88072 | C22 | semidirect |
| 27. #88049 | C22 | semidirect |
| 28. #88048 | C22 | semidirect |
| 29. #88047 | C22 | semidirect |
| 30. #88043 | C22 | semidirect |
| 31. C4×#1055 | C22 | semidirect |
| 36. C2×D4×C13 | C2×C4 | semidirect |
| 42. C2×D52 | C2×C4 | semidirect |
| 53. #6104 | C2×C4 | semidirect |
| 54. #6104 | C2×C4 | semidirect |
| 59. C2×#1055 | C2×C4 | semidirect |
| 91. #518 | D13 | semidirect |
| 123. C4×D4 | C2×D13 | semidirect |
| 148. C2×D4 | C4×D13 | semidirect |
| 171. C13 | #2948 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#518 | 2 |
| C22×#6104 | 2 |
| #11719226 | 2 |
| #11718876 | 2 |
| #11718675 | 2 |
| C4×#6104 | 2 |
| #11718662 | 2 |
| #11718659 | 2 |
| #11718658 | 2 |
| #2948 | 13 |