Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
928 conjugacy classes of subgroups; only the 237 normal subgroups are shown.
This group has 928 conjugacy classes of subgroups — too many to draw. Only its 237 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. C2×C4×D124 | C2 | semidirect |
| 3. #14520955 | C2 | semidirect |
| 4. #14520925 | C2 | semidirect |
| 5. #14520911 | C2 | semidirect |
| 6. #14520909 | C2 | semidirect |
| 7. #95×D31 | C2 | semidirect |
| 8. C4×C22⋊C4×C31 | C2 | semidirect |
| 12. C2×#92495 | C4 | semidirect |
| 31. C22×C4×C31 | C2×C4 | semidirect |
| 37. C2×C22⋊D31 | C2×C4 | semidirect |
| 47. C2×C4×D31 | C2×C4 | semidirect |
| 49. C2×Dic62 | C2×C4 | semidirect |
| 76. C2×C4×C31 | #41 | semidirect |
| 83. D124 | C22⋊C4 | semidirect |
| 115. C4×C22⋊C4 | D31 | semidirect |
| 143. C31 | #2339 | semidirect |
| 161. C22×C4 | C4×D31 | semidirect |
| 201. C2×C4 | #92495 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#92495 | 2 |
| C2×C4×D124 | 2 |
| #14520955 | 2 |
| #14520925 | 2 |
| #14520911 | 2 |
| #14520909 | 2 |
| #95×D31 | 2 |
| C4×C22⋊C4×C31 | 2 |
| #2339 | 31 |