Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
552 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 221 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×#92469 | C2 | semidirect |
| 3. #14521128 | C2 | direct (N × H) |
| 4. C2×C4⋊(C31⋊C8) | C2 | semidirect |
| 5. C2×(C2×D31)⋊C8 | C2 | semidirect |
| 6. C2×C4×C8×C31 | C2 | semidirect |
| 16. C2×#92469 | C22 | semidirect |
| 19. C4×C8×C31 | C22 | semidirect |
| 20. (C2×D31)⋊C8 | C22 | semidirect |
| 21. C4⋊(C31⋊C8) | C22 | semidirect |
| 34. C2×C8×C31 | D4 | semidirect |
| 50. C2×C4×C31 | M16 | semidirect |
| 64. C8×C31 | C2×D4 | semidirect |
| 77. C4×C31 | C2×M16 | semidirect |
| 86. C2×C4×C8 | D31 | semidirect |
| 87. C2×C31 | #436 | semidirect |
| 106. C4×C8 | C2×D31 | semidirect |
| 107. C31 | C2×#436 | semidirect |
| 123. C2×C8 | D124 | semidirect |
| 142. C2×C4 | #92469 | semidirect |
| 151. C8 | C2×D124 | semidirect |
| 163. C4 | C2×#92469 | semidirect |
| 167. C2 | #14521128 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#92469 | 2 |
| C2×C4×D124 | 2 |
| #14521128 | 2 |
| C2×C4⋊(C31⋊C8) | 2 |
| C2×(C2×D31)⋊C8 | 2 |
| C2×C4×C8×C31 | 2 |
| C2×#436 | 31 |