Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
1504 conjugacy classes of subgroups; only the 1077 normal subgroups are shown.
This group has 1504 conjugacy classes of subgroups — too many to draw. Only its 1077 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. C2×#11758525 | C2 | direct (N × H) |
| 2. C22×#92474 | C2 | semidirect |
| 3. C23×C31⋊C8 | C2 | semidirect |
| 10. #11758525 | C22 | direct (N × H) |
| 11. C2×#92474 | C22 | semidirect |
| 14. C22×C31⋊C8 | C22 | semidirect |
| 24. #92474 | C23 | semidirect |
| 27. C2×C31⋊C8 | C23 | semidirect |
| 42. C22×C31 | #131 | semidirect |
| 53. C2×C31 | C2×#131 | semidirect |
| 65. C31 | C22×#131 | semidirect |
| 92. C22 | #11758525 | direct (N × H) |
| 99. C2 | C2×#11758525 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11758525 | 2 |
| C22×#92474 | 2 |
| C23×C31⋊C8 | 2 |
| C22×#41×C31 | 2 |
| C22×#131 | 31 |