Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
364 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 364 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. C2×#11758481 | C2 | semidirect |
| 2. #14521492 | C2 | semidirect |
| 3. #14521487 | C2 | semidirect |
| 4. #14521481 | C2 | semidirect |
| 5. C2×C31×M32 | C2 | semidirect |
| 8. C2×Dic124 | C22 | semidirect |
| 12. #11758481 | C22 | semidirect |
| 13. C2×D248 | C22 | semidirect |
| 15. C31×M32 | C22 | semidirect |
| 16. C2×C16×C31 | C22 | semidirect |
| 17. Dic248 | C22 | semidirect |
| 18. #11758388 | C22 | semidirect |
| 19. D496 | C22 | semidirect |
| 72. C2×M32 | D31 | semidirect |
| 89. M32 | C2×D31 | semidirect |
| 90. C2×C16 | C2×D31 | semidirect |
| 91. C31 | #3414 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11758481 | 2 |
| #14521492 | 2 |
| #14521487 | 2 |
| #14521481 | 2 |
| C2×C31×M32 | 2 |
| #3414 | 31 |