Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
170 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 49 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. #14521484 | C2 | semidirect |
| 2. #14521426 | C2 | semidirect |
| 3. #14520870 | C2 | semidirect |
| 4. #14520861 | C2 | semidirect |
| 5. C31×#443 | C2 | semidirect |
| 20. Q16×C31 | D4 | semidirect |
| 22. D8×C31 | D4 | semidirect |
| 60. #443 | D31 | semidirect |
| 78. C31 | #2213 | semidirect |
| 82. Q16 | D124 | semidirect |
| 88. D8 | D124 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14521484 | 2 |
| #14521426 | 2 |
| #14520870 | 2 |
| #14520861 | 2 |
| C31×#443 | 2 |
| #2213 | 31 |