Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
488 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 133 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×#11758485 | C2 | semidirect |
| 2. C2×#11758509 | C2 | semidirect |
| 3. C22×#92479 | C2 | semidirect |
| 4. C2×#11758484 | C2 | semidirect |
| 5. #14521318 | C2 | direct (N × H) |
| 6. C2×#11758410 | C2 | semidirect |
| 7. C2×#11758411 | C2 | semidirect |
| 8. C2×C31×#100 | C2 | semidirect |
| 16. #11758509 | C22 | semidirect |
| 21. C2×#92479 | C22 | semidirect |
| 25. #11758485 | C22 | semidirect |
| 27. #11758484 | C22 | semidirect |
| 32. C31×#100 | C22 | semidirect |
| 33. #11758411 | C22 | semidirect |
| 34. #11758410 | C22 | semidirect |
| 144. C2×#100 | D31 | semidirect |
| 148. C2×C31 | #472 | semidirect |
| 177. #100 | C2×D31 | semidirect |
| 178. C31 | C2×#472 | semidirect |
| 285. C2 | #14521318 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11758485 | 2 |
| C2×#11758509 | 2 |
| C22×#92479 | 2 |
| C2×#11758484 | 2 |
| #14521318 | 2 |
| C2×#11758410 | 2 |
| C2×#11758411 | 2 |
| C2×C31×#100 | 2 |
| C2×#472 | 31 |