Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
396 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 117 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. #14521772 | C2 | semidirect |
| 3. #14521396 | C2 | semidirect |
| 4. #14521376 | C2 | semidirect |
| 5. #14521334 | C2 | semidirect |
| 6. #14521281 | C2 | semidirect |
| 7. #14521249 | C2 | semidirect |
| 8. #14521210 | C2 | semidirect |
| 9. C8×D124 | C2 | semidirect |
| 10. #14521044 | C2 | semidirect |
| 11. C4×Q16×C31 | C2 | semidirect |
| 131. C4×Q16 | D31 | semidirect |
| 168. C31 | #3304 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14521772 | 2 |
| #14521721 | 2 |
| #14521396 | 2 |
| #14521376 | 2 |
| #14521334 | 2 |
| #14521281 | 2 |
| #14521249 | 2 |
| #14521210 | 2 |
| C8×D124 | 2 |
| #14521044 | 2 |
| C4×Q16×C31 | 2 |
| #3304 | 31 |