Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
360 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 125 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×#11758395 | C2 | semidirect |
| 4. #14520811 | C2 | semidirect |
| 16. C22⋊(C31⋊C8) | C4 | semidirect |
| 39. C2×C31⋊C8 | C2×C4 | semidirect |
| 75. C22×C31 | #107 | semidirect |
| 114. C31 | #1852 | semidirect |
| 171. C22 | #11758395 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11758395 | 2 |
| C2×C22⋊(C31⋊C8) | 2 |
| #14520909 | 2 |
| #14520811 | 2 |
| C22×C4⋊C4×C31 | 2 |
| #1852 | 31 |