Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
452 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 123 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. #14521845 | C2 | semidirect |
| 2. C2×#11758489 | C2 | semidirect |
| 3. #131×D31 | C2 | semidirect |
| 4. #14521325 | C2 | semidirect |
| 5. #14521324 | C2 | semidirect |
| 6. #14521316 | C2 | semidirect |
| 7. #14521311 | C2 | semidirect |
| 8. #14521310 | C2 | semidirect |
| 9. #108×D31 | C2 | semidirect |
| 10. #14521030 | C2 | semidirect |
| 11. C31×#472 | C2 | semidirect |
| 15. C2×D8×C31 | C22 | semidirect |
| 19. C2×#92480 | C22 | semidirect |
| 35. C2×Dic124 | C22 | semidirect |
| 40. C31×#108 | C22 | semidirect |
| 41. C31×#100 | C22 | semidirect |
| 42. #11758421 | C22 | semidirect |
| 43. #11758412 | C22 | semidirect |
| 44. #11758412 | C22 | semidirect |
| 45. #11758410 | C22 | semidirect |
| 46. #11758407 | C22 | semidirect |
| 166. #472 | D31 | semidirect |
| 194. C2×D8 | C2×D31 | semidirect |
| 208. #108 | C2×D31 | semidirect |
| 212. #100 | C2×D31 | semidirect |
| 213. C31 | #3067 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14521845 | 2 |
| C2×#11758489 | 2 |
| #131×D31 | 2 |
| #14521325 | 2 |
| #14521324 | 2 |
| #14521316 | 2 |
| #14521311 | 2 |
| #14521310 | 2 |
| #108×D31 | 2 |
| #14521030 | 2 |
| C31×#472 | 2 |
| #3067 | 31 |