Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
1812 conjugacy classes of subgroups; only the 277 normal subgroups are shown.
This group has 1812 conjugacy classes of subgroups — too many to draw. Only its 277 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. C23×D124 | C2 | semidirect |
| 2. C23×C22⋊D31 | C2 | semidirect |
| 3. C22×(C2×D31)⋊C4 | C2 | semidirect |
| 4. #14520958 | C2 | direct (N × H) |
| 5. C2×C31⋊#95 | C2 | semidirect |
| 6. C22×C22⋊C4×C31 | C2 | semidirect |
| 14. C22×C22⋊D31 | C22 | semidirect |
| 18. C22×D124 | C22 | semidirect |
| 20. C2×C22⋊C4×C31 | C22 | semidirect |
| 22. C2×(C2×D31)⋊C4 | C22 | semidirect |
| 23. C31⋊#95 | C22 | semidirect |
| 28. C24×C31 | D4 | semidirect |
| 37. C23×D31 | D4 | semidirect |
| 42. C22×C4×C31 | D4 | semidirect |
| 51. C22×Dic31 | D4 | semidirect |
| 71. C23×C31 | C2×D4 | semidirect |
| 87. C22×D31 | C2×D4 | semidirect |
| 93. C2×C4×C31 | C2×D4 | semidirect |
| 98. C2×Dic31 | C2×D4 | semidirect |
| 131. C22×C22⋊C4 | D31 | semidirect |
| 135. C2×C31 | #392 | semidirect |
| 157. C2×C22⋊C4 | C2×D31 | semidirect |
| 159. C31 | C2×#392 | semidirect |
| 172. C24 | D124 | semidirect |
| 189. C22×C4 | C22⋊D31 | semidirect |
| 218. C23 | C2×D124 | semidirect |
| 235. C2×C4 | C2×C22⋊D31 | semidirect |
| 265. C2 | #14520958 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D124 | 2 |
| C23×C22⋊D31 | 2 |
| C22×(C2×D31)⋊C4 | 2 |
| #14520958 | 2 |
| C2×C31⋊#95 | 2 |
| C22×C22⋊C4×C31 | 2 |
| C2×#392 | 31 |