Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
760 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 760 conjugacy classes of subgroups — too many to draw. Only its 181 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×D248 | C2 | semidirect |
| 2. C22×#92479 | C2 | semidirect |
| 3. C2×#11758517 | C2 | semidirect |
| 4. #14521424 | C2 | direct (N × H) |
| 5. C2×C8×Dic31 | C2 | semidirect |
| 6. C22×D8×C31 | C2 | semidirect |
| 11. C2×D8×C31 | C22 | semidirect |
| 14. #11758517 | C22 | semidirect |
| 16. C2×#92479 | C22 | semidirect |
| 20. C2×D248 | C22 | semidirect |
| 21. C8×Dic31 | C22 | semidirect |
| 37. C2×C8×C31 | D4 | semidirect |
| 42. C2×C31⋊C8 | D4 | semidirect |
| 60. C2×Dic31 | D8 | semidirect |
| 65. C8×C31 | C2×D4 | semidirect |
| 66. C31⋊C8 | C2×D4 | semidirect |
| 80. Dic31 | C2×D8 | semidirect |
| 83. C22×D8 | D31 | semidirect |
| 88. C2×C31 | #493 | semidirect |
| 100. C2×D8 | C2×D31 | semidirect |
| 107. C31 | C2×#493 | semidirect |
| 127. C2×C8 | C22⋊D31 | semidirect |
| 152. C8 | C2×C22⋊D31 | semidirect |
| 168. C2 | #14521424 | 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 |
| C22×#92479 | 2 |
| C2×#11758517 | 2 |
| #14521424 | 2 |
| C2×C8×Dic31 | 2 |
| C22×D8×C31 | 2 |
| C2×#493 | 31 |