Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
360 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 101 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 |
| 3. C2×#11758393 | C2 | semidirect |
| 4. C43×C31 | C2 | semidirect |
| 11. #11758452 | C4 | semidirect |
| 12. #11758451 | C4 | semidirect |
| 14. #11758446 | C4 | semidirect |
| 32. C42×C31 | D4 | semidirect |
| 64. C4×C31 | #104 | semidirect |
| 72. C43 | D31 | semidirect |
| 89. C31 | #1962 | semidirect |
| 109. C42 | D124 | semidirect |
| 137. C4 | #11758393 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14521599 | 2 |
| #14521073 | 2 |
| C2×#11758393 | 2 |
| C43×C31 | 2 |
| #1962 | 31 |