Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
230 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 53 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×#11758481 | C2 | semidirect |
| 2. C2×#11758388 | C2 | semidirect |
| 3. C2×D496 | C2 | semidirect |
| 4. #14521285 | C2 | semidirect |
| 5. #14520854 | C2 | semidirect |
| 6. #14520851 | C2 | semidirect |
| 7. C31×C22⋊C16 | C2 | semidirect |
| 39. Dic124 | D4 | semidirect |
| 43. D248 | D4 | semidirect |
| 90. C22⋊C16 | D31 | semidirect |
| 112. C31 | #2186 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11758481 | 2 |
| C2×#11758388 | 2 |
| C2×D496 | 2 |
| #14521285 | 2 |
| #14520854 | 2 |
| #14520851 | 2 |
| C31×C22⋊C16 | 2 |
| #2186 | 31 |