Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
996 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 996 conjugacy classes of subgroups — too many to draw. Only its 181 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 |
|---|---|---|
| 2. C22×#92470 | C2 | semidirect |
| 3. C2×#11758501 | C2 | semidirect |
| 4. #14521202 | C2 | direct (N × H) |
| 5. C2×#11758409 | C2 | semidirect |
| 6. C2×C31×C22⋊C8 | C2 | semidirect |
| 14. C22×Dic62 | C22 | semidirect |
| 15. C22×C8×C31 | C22 | semidirect |
| 17. C2×C4⋊Dic31 | C22 | semidirect |
| 19. #11758501 | C22 | semidirect |
| 22. C2×#92470 | C22 | semidirect |
| 23. C31×C22⋊C8 | C22 | semidirect |
| 24. #11758409 | C22 | semidirect |
| 48. C2×Dic62 | C23 | semidirect |
| 50. C2×C8×C31 | C23 | semidirect |
| 53. C4⋊Dic31 | C23 | semidirect |
| 58. C23×C31 | SD16 | semidirect |
| 93. C22×C31 | C2×SD16 | semidirect |
| 111. C2×C22⋊C8 | D31 | semidirect |
| 113. C2×C31 | #450 | semidirect |
| 128. C22×C8 | C2×D31 | semidirect |
| 135. C22⋊C8 | C2×D31 | semidirect |
| 136. C31 | C2×#450 | semidirect |
| 163. C2×C8 | C22×D31 | semidirect |
| 178. C23 | #92470 | semidirect |
| 209. C22 | C2×#92470 | semidirect |
| 219. C2 | #14521202 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D124 | 2 |
| C22×#92470 | 2 |
| C2×#11758501 | 2 |
| #14521202 | 2 |
| C2×#11758409 | 2 |
| C2×C31×C22⋊C8 | 2 |
| C2×#450 | 31 |