Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
616 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 616 conjugacy classes of subgroups — too many to draw. Only its 205 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. C2×#11758470 | C2 | semidirect |
| 3. #14521131 | C2 | direct (N × H) |
| 4. C2×#11758397 | C2 | semidirect |
| 5. C2×C8×Dic31 | C2 | semidirect |
| 6. C2×C31×#107 | C2 | semidirect |
| 14. C2×D248 | C4 | semidirect |
| 17. #11758470 | C22 | semidirect |
| 18. C31×#107 | C22 | semidirect |
| 19. C8×Dic31 | C22 | semidirect |
| 20. #11758397 | C22 | semidirect |
| 28. C2×D124 | C2×C4 | semidirect |
| 32. C2×C8×C31 | C2×C4 | semidirect |
| 41. D248 | C2×C4 | semidirect |
| 54. C2×Dic31 | D8 | semidirect |
| 59. D124 | C22×C4 | semidirect |
| 61. C8×C31 | C22×C4 | semidirect |
| 77. Dic31 | C2×D8 | semidirect |
| 81. C2×#107 | D31 | semidirect |
| 84. C2×C31 | C4×D8 | semidirect |
| 100. #107 | C2×D31 | semidirect |
| 103. C31 | C2×C4×D8 | semidirect |
| 118. C2×C8 | C4×D31 | semidirect |
| 145. C8 | C2×C4×D31 | semidirect |
| 161. C2 | #14521131 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D248 | 2 |
| C2×#11758470 | 2 |
| #14521131 | 2 |
| C2×#11758397 | 2 |
| C2×C8×Dic31 | 2 |
| C2×C31×#107 | 2 |
| C2×C4×D8 | 31 |