Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
500 conjugacy classes of subgroups; only the 217 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 217 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. C8×D124 | C2 | semidirect |
| 3. #14521114 | C2 | semidirect |
| 4. #14521102 | C2 | semidirect |
| 5. C22⋊C8×D31 | C2 | semidirect |
| 6. C31×#431 | C2 | semidirect |
| 12. C2×C8×D31 | C22 | semidirect |
| 17. C31×C4⋊C8 | C22 | semidirect |
| 19. C4×C8×C31 | C22 | semidirect |
| 21. (C2×D31)⋊C8 | C22 | semidirect |
| 22. C4⋊(C31⋊C8) | C22 | semidirect |
| 23. C4×C31⋊C8 | C22 | semidirect |
| 29. C2×D124 | C8 | semidirect |
| 49. C22×D31 | C2×C8 | semidirect |
| 53. C2×C4×C31 | C2×C8 | semidirect |
| 62. D124 | C2×C8 | semidirect |
| 63. D124 | C2×C8 | semidirect |
| 88. #431 | D31 | semidirect |
| 106. C4⋊C8 | C2×D31 | semidirect |
| 111. C4×C8 | C2×D31 | semidirect |
| 112. C31 | #2972 | semidirect |
| 148. C2×C4 | C8×D31 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D124 | 2 |
| C8×D124 | 2 |
| #14521114 | 2 |
| #14521102 | 2 |
| C22⋊C8×D31 | 2 |
| C31×#431 | 2 |
| #2972 | 31 |