Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
408 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 105 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×#92469 | C2 | semidirect |
| 3. C2×(C2×D31)⋊C8 | C2 | semidirect |
| 4. C2×(C2×D31)⋊C8 | C2 | semidirect |
| 5. C2×(C2×D31)⋊C8 | C2 | semidirect |
| 6. #14520804 | C2 | semidirect |
| 7. C31×#336 | C2 | semidirect |
| 54. C2×C8×C31 | D4 | semidirect |
| 65. C2×C31⋊C8 | D4 | semidirect |
| 81. C22×D31 | M16 | semidirect |
| 87. C2×C4×C31 | M16 | semidirect |
| 149. #336 | D31 | semidirect |
| 178. C31 | #1870 | semidirect |
| 213. C2×C8 | D124 | semidirect |
| 254. C2×C4 | #92469 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#92469 | 2 |
| C2×C4×D124 | 2 |
| C2×(C2×D31)⋊C8 | 2 |
| #14520804 | 2 |
| C31×#336 | 2 |
| #1870 | 31 |