Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
368 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 117 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×#11758496 | C2 | semidirect |
| 2. #14521482 | C2 | direct (N × H) |
| 3. C2×#11758416 | C2 | semidirect |
| 4. C2×D496 | C2 | semidirect |
| 5. C2×C16×D31 | C2 | semidirect |
| 6. C2×C31×Q32 | C2 | semidirect |
| 11. #11758496 | C22 | semidirect |
| 14. C31×Q32 | C22 | semidirect |
| 16. #11758416 | C22 | semidirect |
| 18. D496 | C22 | semidirect |
| 19. C16×D31 | C22 | semidirect |
| 66. C2×Q32 | D31 | semidirect |
| 70. C2×C31 | #508 | semidirect |
| 81. Q32 | C2×D31 | semidirect |
| 87. C31 | C2×#508 | semidirect |
| 133. C2 | #14521482 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11758496 | 2 |
| #14521482 | 2 |
| C2×#11758416 | 2 |
| C2×D496 | 2 |
| C2×C16×D31 | 2 |
| C2×C31×Q32 | 2 |
| C2×#508 | 31 |