Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
656 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 157 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×#11758509 | C2 | semidirect |
| 2. #14521599 | C2 | semidirect |
| 3. #14521436 | C2 | semidirect |
| 4. #14521425 | C2 | semidirect |
| 5. #14521421 | C2 | semidirect |
| 6. C4×#92474 | C2 | semidirect |
| 7. C2×C31×#127 | C2 | semidirect |
| 15. C2×#92480 | C22 | semidirect |
| 17. C2×#92479 | C22 | semidirect |
| 20. #11758452 | C22 | semidirect |
| 21. #11758451 | C22 | semidirect |
| 23. #11758446 | C22 | semidirect |
| 24. #11758391 | C22 | semidirect |
| 25. C4×C31⋊C8 | C22 | semidirect |
| 48. #92474 | D4 | semidirect |
| 71. C31⋊C8 | C2×D4 | semidirect |
| 83. C4×C31 | AGL(1,ℤ/8) | semidirect |
| 88. C2×#127 | D31 | semidirect |
| 116. C31 | #3151 | semidirect |
| 173. C4 | #11758509 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11758509 | 2 |
| #14521599 | 2 |
| #14521436 | 2 |
| #14521425 | 2 |
| #14521421 | 2 |
| C4×#92474 | 2 |
| C2×C31×#127 | 2 |
| #3151 | 31 |