Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
462 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 462 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. #14521756 | C2 | semidirect |
| 3. #14521396 | C2 | semidirect |
| 4. #14521368 | C2 | semidirect |
| 5. #14521340 | C2 | semidirect |
| 6. #14521278 | C2 | semidirect |
| 7. #14521250 | C2 | semidirect |
| 8. #14521202 | C2 | semidirect |
| 9. C4×#92470 | C2 | semidirect |
| 10. C2×#11758409 | C2 | semidirect |
| 11. C8×D4×C31 | C2 | semidirect |
| 14. C22×C8×C31 | C22 | semidirect |
| 18. C2×C4⋊Dic31 | C22 | semidirect |
| 19. #11758501 | C22 | semidirect |
| 21. C2×#92470 | C22 | semidirect |
| 28. #11758446 | C22 | semidirect |
| 29. C4×Dic62 | 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. #11758405 | C22 | semidirect |
| 39. #11758405 | C22 | semidirect |
| 40. #11758404 | C22 | semidirect |
| 83. D4×C31 | SD16 | semidirect |
| 140. C8×D4 | D31 | semidirect |
| 152. C22×C8 | C2×D31 | semidirect |
| 168. C4⋊C8 | C2×D31 | semidirect |
| 175. C22⋊C8 | C2×D31 | semidirect |
| 176. C4×C8 | C2×D31 | semidirect |
| 177. C31 | #3295 | semidirect |
| 231. D4 | #92470 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14521756 | 2 |
| D4×D124 | 2 |
| #14521396 | 2 |
| #14521368 | 2 |
| #14521340 | 2 |
| #14521278 | 2 |
| #14521250 | 2 |
| #14521202 | 2 |
| C4×#92470 | 2 |
| C2×#11758409 | 2 |
| C8×D4×C31 | 2 |
| #3295 | 31 |