Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
712 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 712 conjugacy classes of subgroups — too many to draw. Only its 149 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×#11758567 | C2 | semidirect |
| 2. C2×#11758486 | C2 | semidirect |
| 3. C2×#11758527 | C2 | semidirect |
| 4. #14521630 | C2 | semidirect |
| 5. #14521212 | C2 | semidirect |
| 6. #14521206 | C2 | semidirect |
| 7. #14521195 | C2 | semidirect |
| 8. #14521189 | C2 | semidirect |
| 9. C2×#11758398 | C2 | semidirect |
| 10. #14521017 | C2 | semidirect |
| 11. C31×#417 | C2 | semidirect |
| 46. #41×C31 | D4 | semidirect |
| 79. C2×Dic62 | D4 | semidirect |
| 171. #417 | D31 | semidirect |
| 214. C31 | #3013 | semidirect |
| 224. #41 | D124 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11758567 | 2 |
| C2×#11758486 | 2 |
| C2×#11758527 | 2 |
| #14521630 | 2 |
| #14521212 | 2 |
| #14521206 | 2 |
| #14521195 | 2 |
| #14521189 | 2 |
| C2×#11758398 | 2 |
| #14521017 | 2 |
| C31×#417 | 2 |
| #3013 | 31 |