Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
656 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 656 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×#92470 | C2 | semidirect |
| 2. C22×#92480 | C2 | semidirect |
| 3. C22×#92481 | C2 | semidirect |
| 4. C2×#11758521 | C2 | semidirect |
| 6. #14521420 | C2 | direct (N × H) |
| 7. C2×C8×Dic31 | C2 | semidirect |
| 8. C22×SD16×C31 | C2 | semidirect |
| 15. C2×SD16×C31 | C22 | semidirect |
| 18. #11758521 | C22 | semidirect |
| 20. C2×#92481 | C22 | semidirect |
| 24. C2×#92480 | C22 | semidirect |
| 29. C2×#92470 | C22 | semidirect |
| 30. C8×Dic31 | C22 | semidirect |
| 56. C2×C8×C31 | D4 | semidirect |
| 63. C2×C31⋊C8 | D4 | semidirect |
| 88. C2×Dic31 | SD16 | semidirect |
| 96. C8×C31 | C2×D4 | semidirect |
| 97. C31⋊C8 | C2×D4 | semidirect |
| 113. Dic31 | C2×SD16 | semidirect |
| 117. C22×SD16 | D31 | semidirect |
| 123. C2×C31 | #492 | semidirect |
| 139. C2×SD16 | C2×D31 | semidirect |
| 149. C31 | C2×#492 | semidirect |
| 180. C2×C8 | C22⋊D31 | semidirect |
| 216. C8 | C2×C22⋊D31 | semidirect |
| 234. C2 | #14521420 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#92470 | 2 |
| C22×#92480 | 2 |
| C22×#92481 | 2 |
| C2×#11758521 | 2 |
| C2×#11758517 | 2 |
| #14521420 | 2 |
| C2×C8×Dic31 | 2 |
| C22×SD16×C31 | 2 |
| C2×#492 | 31 |