Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
456 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 129 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. #14521594 | C2 | semidirect |
| 2. #14521453 | C2 | semidirect |
| 3. #14521424 | C2 | semidirect |
| 4. #14521394 | C2 | semidirect |
| 5. #14521285 | C2 | semidirect |
| 6. #14521283 | C2 | semidirect |
| 7. D8×Dic31 | C2 | semidirect |
| 8. #14521131 | C2 | semidirect |
| 9. #14521129 | C2 | semidirect |
| 10. C2×C8×Dic31 | C2 | semidirect |
| 11. C31×#466 | C2 | semidirect |
| 89. C2×Dic31 | D8 | semidirect |
| 99. C8×C31 | #41 | semidirect |
| 101. C31⋊C8 | #41 | semidirect |
| 128. #466 | D31 | semidirect |
| 166. C31 | #3169 | semidirect |
| 229. C8 | #92497 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14521594 | 2 |
| #14521453 | 2 |
| #14521424 | 2 |
| #14521394 | 2 |
| #14521285 | 2 |
| #14521283 | 2 |
| D8×Dic31 | 2 |
| #14521131 | 2 |
| #14521129 | 2 |
| C2×C8×Dic31 | 2 |
| C31×#466 | 2 |
| #3169 | 31 |