Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
448 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 448 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. C2×#11758447 | C2 | semidirect |
| 3. #14521350 | C2 | direct (N × H) |
| 4. C2×#11758406 | C2 | semidirect |
| 5. C2×#11758405 | C2 | semidirect |
| 8. C2×C31×C4⋊C8 | C2 | semidirect |
| 23. #11758447 | C22 | semidirect |
| 24. C31×C4⋊C8 | C22 | semidirect |
| 27. #11758406 | C22 | semidirect |
| 28. #11758405 | C22 | semidirect |
| 104. C2×C4⋊C8 | D31 | semidirect |
| 107. C2×C31 | #478 | semidirect |
| 129. C4⋊C8 | C2×D31 | semidirect |
| 132. C31 | C2×#478 | semidirect |
| 203. C2 | #14521350 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11758447 | 2 |
| C2×C4×D124 | 2 |
| #14521350 | 2 |
| C2×#11758406 | 2 |
| C2×#11758405 | 2 |
| C2×#11758409 | 2 |
| C2×C31×C4⋊C8 | 2 |
| C2×#478 | 31 |