Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
1880 conjugacy classes of subgroups; only the 1157 normal subgroups are shown.
This group has 1880 conjugacy classes of subgroups — too many to draw. Only its 1157 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×#11758503 | C2 | direct (N × H) |
| 2. C22×C4⋊Dic31 | C2 | semidirect |
| 4. C22×C4×Dic31 | C2 | semidirect |
| 7. C23×C4×C31 | C4 | semidirect |
| 13. #11758503 | C22 | direct (N × H) |
| 14. C2×C4⋊Dic31 | C22 | semidirect |
| 15. C2×C4×Dic31 | C22 | semidirect |
| 22. C22×C4×C31 | C2×C4 | semidirect |
| 29. C4⋊Dic31 | C23 | semidirect |
| 30. C4×Dic31 | C23 | semidirect |
| 40. C2×C4×C31 | C22×C4 | semidirect |
| 48. C22×C31 | #117 | semidirect |
| 62. C2×C31 | C2×#117 | semidirect |
| 67. C23×C4 | Dic31 | semidirect |
| 75. C31 | C22×#117 | semidirect |
| 84. C22×C4 | C2×Dic31 | semidirect |
| 102. C2×C4 | C22×Dic31 | semidirect |
| 107. C22 | #11758503 | direct (N × H) |
| 116. C2 | C2×#11758503 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11758503 | 2 |
| C22×C4⋊Dic31 | 2 |
| C22×C22⋊Dic31 | 2 |
| C22×C4×Dic31 | 2 |
| C24×C4×C31 | 2 |
| C22×#117 | 31 |