Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
564 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 165 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. C22×#92482 | C2 | semidirect |
| 4. C2×#11758521 | C2 | semidirect |
| 6. #14521442 | C2 | direct (N × H) |
| 7. C2×#11758403 | C2 | semidirect |
| 8. C22×Q16×C31 | C2 | semidirect |
| 14. C2×Q16×C31 | C22 | semidirect |
| 19. #11758521 | C22 | semidirect |
| 21. C2×#92482 | C22 | semidirect |
| 30. #11758403 | C22 | semidirect |
| 110. C22×Q16 | D31 | semidirect |
| 117. C2×C31 | #497 | semidirect |
| 128. C2×Q16 | C2×D31 | semidirect |
| 143. C31 | C2×#497 | semidirect |
| 222. C2 | #14521442 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#92482 | 2 |
| C22×#92470 | 2 |
| C22×#92481 | 2 |
| C2×#11758521 | 2 |
| C2×#11758524 | 2 |
| #14521442 | 2 |
| C2×#11758403 | 2 |
| C22×Q16×C31 | 2 |
| C2×#497 | 31 |