Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
396 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 125 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. #14521721 | C2 | semidirect |
| 2. #14521415 | C2 | semidirect |
| 3. #14521397 | C2 | semidirect |
| 4. #14521346 | C2 | semidirect |
| 5. #14521336 | C2 | semidirect |
| 6. #14521244 | C2 | semidirect |
| 7. #14521244 | C2 | semidirect |
| 8. #14521180 | C2 | semidirect |
| 9. #14521159 | C2 | semidirect |
| 10. C4×#92479 | C2 | semidirect |
| 11. C31×#554 | C2 | semidirect |
| 80. D4×C31 | #41 | semidirect |
| 124. #554 | D31 | semidirect |
| 170. C31 | #3366 | semidirect |
| 218. D4 | #92499 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14521721 | 2 |
| #14521415 | 2 |
| #14521397 | 2 |
| #14521346 | 2 |
| #14521336 | 2 |
| #14521244 | 2 |
| #14521180 | 2 |
| #14521159 | 2 |
| C4×#92479 | 2 |
| C31×#554 | 2 |
| #3366 | 31 |