Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
544 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 165 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×#92470 | C2 | semidirect |
| 2. C2×#11758501 | C2 | semidirect |
| 4. #14521295 | C2 | direct (N × H) |
| 5. C2×#11758406 | C2 | semidirect |
| 6. C2×#11758404 | C2 | semidirect |
| 7. C2×#11758409 | C2 | semidirect |
| 8. C22×M16×C31 | C2 | semidirect |
| 14. C2×M16×C31 | C22 | semidirect |
| 24. #11758501 | C22 | semidirect |
| 27. C2×#92470 | C22 | semidirect |
| 28. #11758409 | C22 | semidirect |
| 29. #11758406 | C22 | semidirect |
| 30. #11758404 | C22 | semidirect |
| 54. C2×C8×C31 | D4 | semidirect |
| 97. C8×C31 | C2×D4 | semidirect |
| 119. C22×M16 | D31 | semidirect |
| 127. C2×C31 | #468 | semidirect |
| 139. C2×M16 | C2×D31 | semidirect |
| 154. C31 | C2×#468 | semidirect |
| 179. C2×C8 | C22⋊D31 | semidirect |
| 221. C8 | C2×C22⋊D31 | semidirect |
| 243. C2 | #14521295 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#92470 | 2 |
| C2×#11758501 | 2 |
| C2×#11758507 | 2 |
| #14521295 | 2 |
| C2×#11758406 | 2 |
| C2×#11758404 | 2 |
| C2×#11758409 | 2 |
| C22×M16×C31 | 2 |
| C2×#468 | 31 |