Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
500 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 157 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. C22×Dic124 | C2 | semidirect |
| 4. C2×C4×Dic62 | C2 | semidirect |
| 5. #14521272 | C2 | direct (N × H) |
| 6. C2×#11758404 | C2 | semidirect |
| 8. C2×C31×C4⋊C8 | C2 | semidirect |
| 21. C2×Dic124 | C22 | semidirect |
| 27. C4×Dic62 | C22 | semidirect |
| 28. C31×C4⋊C8 | C22 | semidirect |
| 30. #11758404 | C22 | semidirect |
| 116. C2×C4⋊C8 | D31 | semidirect |
| 119. C2×C31 | #464 | semidirect |
| 143. C4⋊C8 | C2×D31 | semidirect |
| 146. C31 | C2×#464 | semidirect |
| 227. C2 | #14521272 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic124 | 2 |
| C22×#92470 | 2 |
| C2×#11758452 | 2 |
| C2×C4×Dic62 | 2 |
| #14521272 | 2 |
| C2×#11758404 | 2 |
| C2×#11758409 | 2 |
| C2×C31×C4⋊C8 | 2 |
| C2×#464 | 31 |