Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
412 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 412 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. #14521604 | C2 | semidirect |
| 3. #14521422 | C2 | semidirect |
| 4. #14521401 | C2 | semidirect |
| 5. #14521397 | C2 | semidirect |
| 6. #14521279 | C2 | semidirect |
| 7. #14521136 | C2 | semidirect |
| 8. C4×C8×D31 | C2 | semidirect |
| 9. C31×#498 | C2 | semidirect |
| 87. C4×D31 | SD16 | semidirect |
| 89. C8×C31 | #41 | semidirect |
| 110. #498 | D31 | semidirect |
| 147. C31 | #3167 | semidirect |
| 203. C8 | #92499 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14521604 | 2 |
| #14521600 | 2 |
| #14521422 | 2 |
| #14521401 | 2 |
| #14521397 | 2 |
| #14521279 | 2 |
| #14521136 | 2 |
| C4×C8×D31 | 2 |
| C31×#498 | 2 |
| #3167 | 31 |