Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
844 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 844 conjugacy classes of subgroups — too many to draw. Only its 149 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×#11758561 | C2 | semidirect |
| 2. C2×#11758485 | C2 | semidirect |
| 3. C2×#11758517 | C2 | semidirect |
| 4. #14521219 | C2 | direct (N × H) |
| 5. C2×#11758413 | C2 | semidirect |
| 6. C2×C31×#100 | C2 | semidirect |
| 12. #11758561 | C22 | semidirect |
| 16. C22×D124 | C22 | semidirect |
| 17. C2×M16×C31 | C22 | semidirect |
| 19. #11758517 | C22 | semidirect |
| 20. C2×C4×Dic31 | C22 | semidirect |
| 22. #11758485 | C22 | semidirect |
| 25. C31×#100 | C22 | semidirect |
| 26. #11758413 | C22 | semidirect |
| 49. #92495 | D4 | semidirect |
| 54. C2×D124 | D4 | semidirect |
| 55. C2×D124 | C23 | semidirect |
| 57. C2×Dic62 | D4 | semidirect |
| 59. M16×C31 | C23 | semidirect |
| 62. C4×Dic31 | C23 | semidirect |
| 94. D124 | C2×D4 | semidirect |
| 98. Dic62 | C2×D4 | semidirect |
| 125. C2×#100 | D31 | semidirect |
| 129. C2×C31 | #453 | semidirect |
| 147. C2×M16 | C2×D31 | semidirect |
| 152. #100 | C2×D31 | semidirect |
| 153. C31 | C2×#453 | semidirect |
| 188. M16 | C22×D31 | semidirect |
| 251. C2 | #14521219 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11758561 | 2 |
| C2×#11758485 | 2 |
| C2×#11758517 | 2 |
| #14521219 | 2 |
| C2×#11758413 | 2 |
| C2×C31×#100 | 2 |
| C2×#453 | 31 |