Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
572 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 153 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. C2×#11758527 | C2 | semidirect |
| 3. #14521595 | C2 | semidirect |
| 4. #14521434 | C2 | semidirect |
| 5. #14521432 | C2 | semidirect |
| 6. #14521430 | C2 | semidirect |
| 7. #14521427 | C2 | semidirect |
| 8. #14521424 | C2 | semidirect |
| 9. #14521420 | C2 | semidirect |
| 10. C2×C8×Dic31 | C2 | semidirect |
| 11. C2×C31×#135 | C2 | semidirect |
| 58. C2×C8×C31 | D4 | semidirect |
| 71. C2×C31⋊C8 | D4 | semidirect |
| 120. Dic31 | #135 | semidirect |
| 123. C2×#135 | D31 | semidirect |
| 165. C31 | #3147 | semidirect |
| 194. C2×C8 | C22⋊D31 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11758481 | 2 |
| C2×#11758527 | 2 |
| #14521595 | 2 |
| #14521434 | 2 |
| #14521432 | 2 |
| #14521430 | 2 |
| #14521427 | 2 |
| #14521424 | 2 |
| #14521420 | 2 |
| C2×C8×Dic31 | 2 |
| C2×C31×#135 | 2 |
| #3147 | 31 |