Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
496 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 496 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×#11758496 | C2 | semidirect |
| 2. #14521600 | C2 | semidirect |
| 3. C4×#92499 | C2 | semidirect |
| 4. #14521273 | C2 | semidirect |
| 5. #14521267 | C2 | semidirect |
| 6. #14521251 | C2 | semidirect |
| 7. #14521249 | C2 | semidirect |
| 8. #14521245 | C2 | semidirect |
| 9. C4⋊C8×D31 | C2 | semidirect |
| 10. #14521044 | C2 | semidirect |
| 11. C31×#462 | C2 | semidirect |
| 49. #92499 | D4 | semidirect |
| 138. C4×C31 | #135 | semidirect |
| 150. #462 | D31 | semidirect |
| 194. C31 | #3035 | semidirect |
| 292. C4 | #11758496 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11758496 | 2 |
| #14521600 | 2 |
| C4×#92499 | 2 |
| #14521273 | 2 |
| #14521267 | 2 |
| #14521251 | 2 |
| #14521249 | 2 |
| #14521245 | 2 |
| C4⋊C8×D31 | 2 |
| #14521044 | 2 |
| C31×#462 | 2 |
| #3035 | 31 |