Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
422 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 161 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. #14521122 | C2 | semidirect |
| 3. #14521119 | C2 | semidirect |
| 4. C8×D124 | C2 | semidirect |
| 5. #14521114 | C2 | semidirect |
| 6. #14521110 | C2 | semidirect |
| 7. #14521014 | C2 | semidirect |
| 8. C22⋊C8×D31 | C2 | semidirect |
| 9. C31×#433 | C2 | semidirect |
| 13. C2×#92469 | C22 | semidirect |
| 16. C2×C8×D31 | C22 | semidirect |
| 23. C31×C4⋊C8 | C22 | semidirect |
| 25. C31×#97 | C22 | semidirect |
| 26. C4×C8×C31 | C22 | semidirect |
| 30. (C2×D31)⋊C8 | C22 | semidirect |
| 31. (C2×D31)⋊C8 | C22 | semidirect |
| 32. C4⋊(C31⋊C8) | C22 | semidirect |
| 33. #11758391 | C22 | semidirect |
| 34. C4×C31⋊C8 | C22 | semidirect |
| 116. #433 | D31 | semidirect |
| 138. C4⋊C8 | C2×D31 | semidirect |
| 146. #97 | C2×D31 | semidirect |
| 148. C4×C8 | C2×D31 | semidirect |
| 149. C31 | #2977 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14521561 | 2 |
| #14521122 | 2 |
| #14521119 | 2 |
| C8×D124 | 2 |
| #14521114 | 2 |
| #14521110 | 2 |
| #14521014 | 2 |
| C22⋊C8×D31 | 2 |
| C31×#433 | 2 |
| #2977 | 31 |