Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
312 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 2. #14521073 | C2 | semidirect |
| 4. #14520809 | C2 | semidirect |
| 5. C4×C4⋊C4×C31 | C2 | semidirect |
| 14. C4×D124 | C4 | semidirect |
| 15. C4×D124 | C4 | semidirect |
| 18. C4×Dic62 | C4 | semidirect |
| 19. C4×Dic62 | C4 | semidirect |
| 81. D124 | C4⋊C4 | semidirect |
| 87. Dic62 | C4⋊C4 | semidirect |
| 102. C4×C31 | #104 | semidirect |
| 113. C4×C4⋊C4 | D31 | semidirect |
| 139. C31 | #1806 | semidirect |
| 220. C4 | #11758393 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#92495 | 2 |
| #14521073 | 2 |
| C2×#11758393 | 2 |
| #14520809 | 2 |
| C4×C4⋊C4×C31 | 2 |
| #1806 | 31 |