Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
760 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 760 conjugacy classes of subgroups — too many to draw. Only its 213 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. C22×D248 | C2 | semidirect |
| 2. C2×#11758451 | C2 | semidirect |
| 3. #14521426 | C2 | direct (N × H) |
| 4. C2×C4×C8×C31 | C2 | semidirect |
| 10. C2×D248 | C22 | semidirect |
| 12. #11758451 | C22 | semidirect |
| 13. C4×C8×C31 | C22 | semidirect |
| 22. C2×C8×C31 | D4 | semidirect |
| 31. C2×C4×C31 | D8 | semidirect |
| 39. C8×C31 | C2×D4 | semidirect |
| 48. C4×C31 | C2×D8 | semidirect |
| 53. C2×C4×C8 | D31 | semidirect |
| 54. C2×C31 | #493 | semidirect |
| 66. C4×C8 | C2×D31 | semidirect |
| 67. C31 | C2×#493 | semidirect |
| 77. C2×C8 | D124 | semidirect |
| 88. C2×C4 | D248 | semidirect |
| 93. C8 | C2×D124 | semidirect |
| 101. C4 | C2×D248 | semidirect |
| 104. C2 | #14521426 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D248 | 2 |
| C2×#11758451 | 2 |
| #14521426 | 2 |
| C2×C4×C8×C31 | 2 |
| C2×#493 | 31 |