Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
512 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 229 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 |
|---|---|---|
| 3. #14521086 | C2 | direct (N × H) |
| 4. C2×#11758406 | C2 | semidirect |
| 5. C2×#11758396 | C2 | semidirect |
| 6. C2×C31×#107 | C2 | semidirect |
| 14. C2×C8×D31 | C4 | semidirect |
| 18. C31×#107 | C22 | semidirect |
| 19. #11758406 | C22 | semidirect |
| 20. #11758396 | C22 | semidirect |
| 40. C8×D31 | C2×C4 | semidirect |
| 80. C2×#107 | D31 | semidirect |
| 82. C2×C31 | #427 | semidirect |
| 99. #107 | C2×D31 | semidirect |
| 101. C31 | C2×#427 | semidirect |
| 157. C2 | #14521086 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C8×D31 | 2 |
| C2×#11758469 | 2 |
| #14521086 | 2 |
| C2×#11758406 | 2 |
| C2×#11758396 | 2 |
| C2×C31×#107 | 2 |
| C2×#427 | 31 |