Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
996 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 996 conjugacy classes of subgroups — too many to draw. Only its 197 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. C22×#92480 | C2 | semidirect |
| 2. C2×#11758501 | C2 | semidirect |
| 3. #14521200 | C2 | direct (N × H) |
| 4. C2×#11758420 | C2 | semidirect |
| 5. C2×C22⋊(C31⋊C8) | C2 | semidirect |
| 14. C22×Dic62 | C22 | semidirect |
| 17. C2×#92480 | C22 | semidirect |
| 18. C2×C4⋊Dic31 | C22 | semidirect |
| 20. #11758501 | C22 | semidirect |
| 22. C22×C31⋊C8 | C22 | semidirect |
| 23. #11758420 | C22 | semidirect |
| 24. C22⋊(C31⋊C8) | C22 | semidirect |
| 48. C2×Dic62 | C23 | semidirect |
| 52. C4⋊Dic31 | C23 | semidirect |
| 55. C2×C31⋊C8 | C23 | semidirect |
| 66. C23×C31 | SD16 | semidirect |
| 98. C22×C31 | C2×SD16 | semidirect |
| 114. C2×C31 | #450 | semidirect |
| 136. C31 | C2×#450 | semidirect |
| 178. C23 | #92480 | semidirect |
| 209. C22 | C2×#92480 | semidirect |
| 219. C2 | #14521200 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#92480 | 2 |
| C2×#11758501 | 2 |
| #14521200 | 2 |
| C2×#11758420 | 2 |
| C2×C22⋊(C31⋊C8) | 2 |
| C23×D4×C31 | 2 |
| C2×#450 | 31 |