Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
488 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 129 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. #14521599 | C2 | semidirect |
| 2. C2×C4×D124 | C2 | semidirect |
| 3. #14521368 | C2 | semidirect |
| 4. #14521340 | C2 | semidirect |
| 5. #14521245 | C2 | semidirect |
| 6. #14521185 | C2 | semidirect |
| 7. #14521162 | C2 | semidirect |
| 8. C31×#432 | C2 | semidirect |
| 19. #11758451 | C22 | semidirect |
| 25. C4×D124 | C22 | semidirect |
| 26. #11758446 | C22 | semidirect |
| 27. C31×C4⋊C8 | C22 | semidirect |
| 29. C31×#97 | C22 | semidirect |
| 31. #11758409 | C22 | semidirect |
| 32. #11758405 | C22 | semidirect |
| 89. D124 | #41 | semidirect |
| 122. #432 | D31 | semidirect |
| 148. C4⋊C8 | C2×D31 | semidirect |
| 152. #97 | C2×D31 | semidirect |
| 153. C31 | #3109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14521599 | 2 |
| C2×C4×D124 | 2 |
| #14521368 | 2 |
| #14521340 | 2 |
| #14521245 | 2 |
| #14521185 | 2 |
| #14521162 | 2 |
| C31×#432 | 2 |
| #3109 | 31 |