Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
1048 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 1048 conjugacy classes of subgroups — too many to draw. Only its 197 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×#92479 | C2 | semidirect |
| 2. C2×#11758507 | C2 | semidirect |
| 3. #14521183 | C2 | direct (N × H) |
| 4. C2×#11758420 | C2 | semidirect |
| 5. C2×C22⋊(C31⋊C8) | C2 | semidirect |
| 6. C23×D4×C31 | C2 | semidirect |
| 12. C22×D4×C31 | C22 | semidirect |
| 15. C22×D124 | C22 | semidirect |
| 17. C2×#92479 | C22 | semidirect |
| 19. #11758507 | C22 | semidirect |
| 21. C2×C4⋊Dic31 | C22 | semidirect |
| 22. C22×C31⋊C8 | C22 | semidirect |
| 23. #11758420 | C22 | semidirect |
| 24. C22⋊(C31⋊C8) | C22 | semidirect |
| 38. C2×D4×C31 | D4 | semidirect |
| 50. C2×D124 | C23 | semidirect |
| 54. C4⋊Dic31 | C23 | semidirect |
| 56. C2×C31⋊C8 | C23 | semidirect |
| 67. C23×C31 | D8 | semidirect |
| 77. D4×C31 | C2×D4 | semidirect |
| 102. C22×C31 | C2×D8 | semidirect |
| 113. C23×D4 | D31 | semidirect |
| 121. C2×C31 | #447 | semidirect |
| 133. C22×D4 | C2×D31 | semidirect |
| 144. C31 | C2×#447 | semidirect |
| 163. C2×D4 | C22⋊D31 | semidirect |
| 191. C23 | #92479 | semidirect |
| 200. D4 | C2×C22⋊D31 | semidirect |
| 224. C22 | C2×#92479 | semidirect |
| 235. C2 | #14521183 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#92479 | 2 |
| C2×#11758507 | 2 |
| #14521183 | 2 |
| C2×#11758420 | 2 |
| C2×C22⋊(C31⋊C8) | 2 |
| C23×D4×C31 | 2 |
| C2×#447 | 31 |