Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
340 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 79 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. #14521815 | C2 | semidirect |
| 3. #14521031 | C2 | semidirect |
| 4. C2×#11758411 | C2 | semidirect |
| 5. C2×#11758411 | C2 | semidirect |
| 6. #14520819 | C2 | semidirect |
| 7. C31×#344 | C2 | semidirect |
| 46. M16×C31 | D4 | semidirect |
| 56. #92474 | D4 | semidirect |
| 115. #344 | D31 | semidirect |
| 140. C31 | #1914 | semidirect |
| 166. M16 | D124 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14521815 | 2 |
| #14521618 | 2 |
| #14521031 | 2 |
| C2×#11758411 | 2 |
| #14520819 | 2 |
| C31×#344 | 2 |
| #1914 | 31 |