Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
494 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 133 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×#11758481 | C2 | semidirect |
| 2. #14521720 | C2 | semidirect |
| 3. #14521704 | C2 | semidirect |
| 4. #14521422 | C2 | semidirect |
| 5. #14521278 | C2 | semidirect |
| 6. #14521260 | C2 | semidirect |
| 7. #14521245 | C2 | semidirect |
| 8. #14521213 | C2 | semidirect |
| 9. #14521196 | C2 | semidirect |
| 10. C4×#92470 | C2 | semidirect |
| 11. C8×D4×C31 | C2 | semidirect |
| 81. #92470 | D4 | semidirect |
| 128. C4×C31 | #135 | semidirect |
| 145. C8×D4 | D31 | semidirect |
| 182. C31 | #3284 | semidirect |
| 272. C4 | #11758481 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11758481 | 2 |
| #14521720 | 2 |
| #14521704 | 2 |
| #14521422 | 2 |
| #14521278 | 2 |
| #14521260 | 2 |
| #14521245 | 2 |
| #14521213 | 2 |
| #14521196 | 2 |
| C4×#92470 | 2 |
| C8×D4×C31 | 2 |
| #3284 | 31 |