Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
386 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 386 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×C4×Dic62 | C2 | semidirect |
| 2. #14521382 | C2 | semidirect |
| 4. #14521353 | C2 | semidirect |
| 5. #14521268 | C2 | semidirect |
| 6. #14521204 | C2 | semidirect |
| 8. #14521154 | C2 | semidirect |
| 9. #14521149 | C2 | semidirect |
| 10. #14521106 | C2 | semidirect |
| 174. C31 | #3117 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×Dic62 | 2 |
| #14521382 | 2 |
| #14521365 | 2 |
| #14521353 | 2 |
| #14521268 | 2 |
| #14521204 | 2 |
| #14521187 | 2 |
| #14521154 | 2 |
| #14521149 | 2 |
| #14521106 | 2 |
| C31×#529 | 2 |
| #3117 | 31 |