Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
548 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 131 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. C2×#11758488 | C2 | semidirect |
| 2. #14521597 | C2 | semidirect |
| 3. C4×D4×D31 | C2 | semidirect |
| 4. #14521263 | C2 | semidirect |
| 5. #14521262 | C2 | semidirect |
| 6. #14521255 | C2 | semidirect |
| 7. #14521254 | C2 | semidirect |
| 8. #14521241 | C2 | semidirect |
| 9. #14521071 | C2 | semidirect |
| 10. #14521047 | C2 | semidirect |
| 11. C31×#459 | C2 | semidirect |
| 16. C31×#127 | C22 | semidirect |
| 20. #11758513 | C22 | semidirect |
| 36. #11758446 | C22 | semidirect |
| 37. C31×C4⋊C8 | C22 | semidirect |
| 38. C31×#102 | C22 | semidirect |
| 39. #11758420 | C22 | semidirect |
| 40. #11758404 | C22 | semidirect |
| 41. Dic31⋊C8 | C22 | semidirect |
| 42. #11758398 | C22 | semidirect |
| 43. C4⋊(C31⋊C8) | C22 | semidirect |
| 57. D4×D31 | D4 | semidirect |
| 146. C4×C31 | AGL(1,ℤ/8) | semidirect |
| 162. #459 | D31 | semidirect |
| 182. #127 | C2×D31 | semidirect |
| 199. C4⋊C8 | C2×D31 | semidirect |
| 203. #102 | C2×D31 | semidirect |
| 204. C31 | #3036 | semidirect |
| 311. C4 | #11758488 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11758488 | 2 |
| #14521597 | 2 |
| C4×D4×D31 | 2 |
| #14521263 | 2 |
| #14521262 | 2 |
| #14521255 | 2 |
| #14521254 | 2 |
| #14521241 | 2 |
| #14521071 | 2 |
| #14521047 | 2 |
| C31×#459 | 2 |
| #3036 | 31 |