Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
388 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 131 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. #14521604 | C2 | semidirect |
| 3. #14521354 | C2 | semidirect |
| 4. #14521348 | C2 | semidirect |
| 5. #14521344 | C2 | semidirect |
| 6. #14521340 | C2 | semidirect |
| 7. #14521326 | C2 | semidirect |
| 8. #14521084 | C2 | semidirect |
| 9. C4⋊C8×D31 | C2 | semidirect |
| 11. C31×#475 | C2 | semidirect |
| 46. #92499 | Q8 | semidirect |
| 136. #475 | D31 | semidirect |
| 177. C31 | #3076 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14521604 | 2 |
| C4×#92499 | 2 |
| #14521354 | 2 |
| #14521348 | 2 |
| #14521344 | 2 |
| #14521340 | 2 |
| #14521326 | 2 |
| #14521084 | 2 |
| C4⋊C8×D31 | 2 |
| #14521044 | 2 |
| C31×#475 | 2 |
| #3076 | 31 |