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×#11758493 | C2 | semidirect |
| 2. #14521600 | C2 | semidirect |
| 3. C4×#92497 | C2 | semidirect |
| 4. #14521274 | C2 | semidirect |
| 5. #14521266 | C2 | semidirect |
| 6. #14521256 | C2 | semidirect |
| 7. #14521250 | C2 | semidirect |
| 8. #14521244 | C2 | semidirect |
| 9. C4⋊C8×D31 | C2 | semidirect |
| 10. #14521044 | C2 | semidirect |
| 11. C31×#461 | C2 | semidirect |
| 53. #92497 | D4 | semidirect |
| 137. C4×C31 | #135 | semidirect |
| 151. #461 | D31 | semidirect |
| 194. C31 | #3035 | semidirect |
| 292. C4 | #11758493 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11758493 | 2 |
| #14521600 | 2 |
| C4×#92497 | 2 |
| #14521274 | 2 |
| #14521266 | 2 |
| #14521256 | 2 |
| #14521250 | 2 |
| #14521244 | 2 |
| C4⋊C8×D31 | 2 |
| #14521044 | 2 |
| C31×#461 | 2 |
| #3035 | 31 |