Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
456 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 149 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. #14521599 | C2 | semidirect |
| 2. #14521454 | C2 | semidirect |
| 3. #14521426 | C2 | semidirect |
| 4. #14521396 | C2 | semidirect |
| 5. #14521285 | C2 | semidirect |
| 6. C4×D248 | C2 | semidirect |
| 7. C2×C4×C8×C31 | C2 | semidirect |
| 50. C2×C4×C31 | D8 | semidirect |
| 65. C8×C31 | #41 | semidirect |
| 87. C2×C4×C8 | D31 | semidirect |
| 109. C31 | #3169 | semidirect |
| 143. C2×C4 | D248 | semidirect |
| 151. C8 | #92495 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14521599 | 2 |
| #14521454 | 2 |
| #14521426 | 2 |
| #14521396 | 2 |
| #14521285 | 2 |
| C4×D248 | 2 |
| C2×C4×C8×C31 | 2 |
| #3169 | 31 |