Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
430 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 119 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. #14521597 | C2 | semidirect |
| 2. C4×#92499 | C2 | semidirect |
| 3. #14521371 | C2 | semidirect |
| 4. #14521334 | C2 | semidirect |
| 5. #14521330 | C2 | semidirect |
| 6. #14521241 | C2 | semidirect |
| 7. #14521193 | C2 | semidirect |
| 8. #14521158 | C2 | semidirect |
| 9. #14521150 | C2 | semidirect |
| 10. #14521105 | C2 | semidirect |
| 11. C31×#460 | C2 | semidirect |
| 87. Q8×C31 | #41 | semidirect |
| 106. D124 | #41 | semidirect |
| 144. #460 | D31 | semidirect |
| 187. C31 | #3115 | semidirect |
| 233. Q8 | #92497 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14521597 | 2 |
| C4×#92499 | 2 |
| #14521371 | 2 |
| #14521334 | 2 |
| #14521330 | 2 |
| #14521241 | 2 |
| #14521193 | 2 |
| #14521158 | 2 |
| #14521150 | 2 |
| #14521105 | 2 |
| C31×#460 | 2 |
| #3115 | 31 |