Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
494 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 139 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. #14521703 | C2 | semidirect |
| 2. D4×D124 | C2 | semidirect |
| 3. #14521396 | C2 | semidirect |
| 4. #14521363 | C2 | semidirect |
| 5. #14521330 | C2 | semidirect |
| 6. #14521285 | C2 | semidirect |
| 7. #14521245 | C2 | semidirect |
| 8. #14521185 | C2 | semidirect |
| 9. C4×D248 | C2 | semidirect |
| 10. C2×#11758409 | C2 | semidirect |
| 11. C8×D4×C31 | C2 | semidirect |
| 15. C22×C8×C31 | C22 | semidirect |
| 18. #11758507 | C22 | semidirect |
| 19. C2×C4⋊Dic31 | C22 | semidirect |
| 21. C2×D248 | C22 | semidirect |
| 28. C4×D124 | C22 | semidirect |
| 29. #11758446 | C22 | semidirect |
| 30. C31×C4⋊C8 | C22 | semidirect |
| 31. C31×C22⋊C8 | C22 | semidirect |
| 32. C4×C8×C31 | C22 | semidirect |
| 35. #11758409 | C22 | semidirect |
| 36. #11758409 | C22 | semidirect |
| 37. #11758409 | C22 | semidirect |
| 38. #11758409 | C22 | semidirect |
| 39. #11758406 | C22 | semidirect |
| 40. #11758406 | C22 | semidirect |
| 85. D4×C31 | D8 | semidirect |
| 106. D124 | #41 | semidirect |
| 145. C8×D4 | D31 | semidirect |
| 159. C22×C8 | C2×D31 | semidirect |
| 174. C4⋊C8 | C2×D31 | semidirect |
| 181. C22⋊C8 | C2×D31 | semidirect |
| 182. C4×C8 | C2×D31 | semidirect |
| 183. C31 | #3294 | semidirect |
| 240. D4 | D248 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14521703 | 2 |
| D4×D124 | 2 |
| #14521396 | 2 |
| #14521363 | 2 |
| #14521330 | 2 |
| #14521285 | 2 |
| #14521245 | 2 |
| #14521185 | 2 |
| C4×D248 | 2 |
| C2×#11758409 | 2 |
| C8×D4×C31 | 2 |
| #3294 | 31 |