Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
1320 conjugacy classes of subgroups; only the 565 normal subgroups are shown.
This group has 1320 conjugacy classes of subgroups — too many to draw. Only its 565 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. C2×#11758475 | C2 | direct (N × H) |
| 2. C22×C4⋊Dic31 | C2 | semidirect |
| 3. C22×Dic31⋊C4 | C2 | semidirect |
| 7. C22×C4×Dic31 | C2 | semidirect |
| 8. C22×C4⋊C4×C31 | C2 | semidirect |
| 16. C2×C4⋊C4×C31 | C22 | semidirect |
| 20. C2×C4⋊Dic31 | C22 | semidirect |
| 21. C2×Dic31⋊C4 | C22 | semidirect |
| 22. C2×C4×Dic31 | C22 | semidirect |
| 23. #11758475 | C22 | direct (N × H) |
| 41. C4⋊C4×C31 | C23 | semidirect |
| 45. C4⋊Dic31 | C23 | semidirect |
| 46. Dic31⋊C4 | C23 | semidirect |
| 47. C4×Dic31 | C23 | semidirect |
| 70. C22×C31 | #126 | semidirect |
| 88. C22×C4⋊C4 | D31 | semidirect |
| 93. C2×C31 | C2×#126 | semidirect |
| 108. C2×C4⋊C4 | C2×D31 | semidirect |
| 113. C31 | C22×#126 | semidirect |
| 133. C4⋊C4 | C22×D31 | semidirect |
| 163. C22 | #11758475 | direct (N × H) |
| 175. C2 | C2×#11758475 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11758475 | 2 |
| C22×C4⋊Dic31 | 2 |
| C22×Dic31⋊C4 | 2 |
| C22×(C2×D31)⋊C4 | 2 |
| C22×C4×Dic31 | 2 |
| C22×C4⋊C4×C31 | 2 |
| C22×#126 | 31 |