Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
160 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 61 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 |
|---|---|---|
| 3. #14520874 | C2 | semidirect |
| 4. #14520853 | C2 | semidirect |
| 6. #14520825 | C2 | semidirect |
| 7. C4×Q16×C31 | C2 | semidirect |
| 15. #11758416 | C4 | semidirect |
| 24. Q16×C31 | C2×C4 | semidirect |
| 36. C31⋊C16 | C2×C4 | semidirect |
| 65. C4×Q16 | D31 | semidirect |
| 87. C31 | #2175 | semidirect |
| 92. Q16 | C4×D31 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11758416 | 2 |
| C4×D248 | 2 |
| #14520874 | 2 |
| #14520853 | 2 |
| #14520849 | 2 |
| #14520825 | 2 |
| C4×Q16×C31 | 2 |
| #2175 | 31 |