Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
360 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 360 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. #14521854 | C2 | semidirect |
| 2. #14521490 | C2 | semidirect |
| 3. #14521484 | C2 | semidirect |
| 4. #14521479 | C2 | semidirect |
| 5. C2×#11758416 | C2 | semidirect |
| 6. #14521466 | C2 | semidirect |
| 7. C31×#578 | C2 | semidirect |
| 11. C31×#135 | C22 | semidirect |
| 12. C2×Q16×C31 | C22 | semidirect |
| 17. #11758417 | C22 | semidirect |
| 18. #11758416 | C22 | semidirect |
| 19. #11758416 | C22 | semidirect |
| 20. #11758415 | C22 | semidirect |
| 21. #11758414 | C22 | semidirect |
| 22. #11758400 | C22 | semidirect |
| 23. C2×C31⋊C16 | C22 | semidirect |
| 71. #578 | D31 | semidirect |
| 87. #135 | C2×D31 | semidirect |
| 88. C2×Q16 | C2×D31 | semidirect |
| 98. C31 | #3416 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14521854 | 2 |
| #14521490 | 2 |
| #14521484 | 2 |
| #14521479 | 2 |
| C2×#11758416 | 2 |
| #14521466 | 2 |
| C31×#578 | 2 |
| #3416 | 31 |