Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
224 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 69 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. #14521452 | C2 | semidirect |
| 3. #14521422 | C2 | semidirect |
| 4. #14521397 | C2 | semidirect |
| 5. #14521395 | C2 | semidirect |
| 6. C8×C31⋊C8 | C2 | semidirect |
| 7. C31×#492 | C2 | semidirect |
| 55. C8×C31 | D8 | semidirect |
| 57. C31⋊C8 | SD16 | semidirect |
| 74. #492 | D31 | semidirect |
| 96. C31 | #1706 | semidirect |
| 133. C8 | #92479 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14521452 | 2 |
| #14521425 | 2 |
| #14521422 | 2 |
| #14521397 | 2 |
| #14521395 | 2 |
| C8×C31⋊C8 | 2 |
| C31×#492 | 2 |
| #1706 | 31 |