Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
572 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 141 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×#11758496 | C2 | semidirect |
| 2. C2×#11758493 | C2 | semidirect |
| 3. C2×#11758489 | C2 | semidirect |
| 4. #14521598 | C2 | semidirect |
| 5. #14521433 | C2 | semidirect |
| 6. #14521431 | C2 | semidirect |
| 7. #14521427 | C2 | semidirect |
| 8. #14521424 | C2 | semidirect |
| 9. #14521420 | C2 | semidirect |
| 10. C4×C8×D31 | C2 | semidirect |
| 11. C31×#495 | C2 | semidirect |
| 75. C8×D31 | D4 | semidirect |
| 76. C8×D31 | D4 | semidirect |
| 120. Dic31 | #135 | semidirect |
| 127. #495 | D31 | semidirect |
| 165. C31 | #3147 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11758496 | 2 |
| C2×#11758493 | 2 |
| C2×#11758489 | 2 |
| #14521598 | 2 |
| #14521433 | 2 |
| #14521431 | 2 |
| #14521427 | 2 |
| #14521424 | 2 |
| #14521420 | 2 |
| C4×C8×D31 | 2 |
| C31×#495 | 2 |
| #3147 | 31 |