Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
376 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 133 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. #14521677 | C2 | semidirect |
| 3. #14521355 | C2 | semidirect |
| 4. #14521352 | C2 | semidirect |
| 5. #14521338 | C2 | semidirect |
| 6. #14521333 | C2 | semidirect |
| 7. C2×#11758396 | C2 | semidirect |
| 8. #14521077 | C2 | semidirect |
| 11. C31×#428 | C2 | semidirect |
| 46. #92495 | Q8 | semidirect |
| 125. #428 | D31 | semidirect |
| 164. C31 | #3084 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14521677 | 2 |
| #14521530 | 2 |
| #14521355 | 2 |
| #14521352 | 2 |
| #14521338 | 2 |
| #14521333 | 2 |
| C2×#11758396 | 2 |
| #14521077 | 2 |
| #14521051 | 2 |
| #14521043 | 2 |
| C31×#428 | 2 |
| #3084 | 31 |