Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
400 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 133 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. #14521485 | C2 | direct (N × H) |
| 3. C2×#11758415 | C2 | semidirect |
| 4. C2×#11758414 | C2 | semidirect |
| 5. C2×#11758400 | C2 | semidirect |
| 6. C22×D8×C31 | C2 | semidirect |
| 12. C2×D8×C31 | C22 | semidirect |
| 14. C2×Dic124 | C22 | semidirect |
| 16. #11758481 | C22 | semidirect |
| 17. C2×D248 | C22 | semidirect |
| 19. #11758415 | C22 | semidirect |
| 20. #11758414 | C22 | semidirect |
| 21. #11758400 | C22 | semidirect |
| 22. C2×C31⋊C16 | C22 | semidirect |
| 43. Dic124 | C23 | semidirect |
| 45. D248 | C23 | semidirect |
| 47. C31⋊C16 | C23 | semidirect |
| 84. C22×D8 | D31 | semidirect |
| 91. C2×C31 | #509 | semidirect |
| 104. C2×D8 | C2×D31 | semidirect |
| 110. C31 | C2×#509 | semidirect |
| 173. C2 | #14521485 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11758481 | 2 |
| #14521485 | 2 |
| C2×#11758415 | 2 |
| C2×#11758414 | 2 |
| C2×#11758400 | 2 |
| C22×D8×C31 | 2 |
| C2×#509 | 31 |