Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
440 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 149 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. C22×D248 | C2 | semidirect |
| 2. C2×#11758414 | C2 | direct (N × H) |
| 3. C22×C31⋊C16 | C2 | semidirect |
| 4. C22×D8×C31 | C2 | semidirect |
| 8. C2×D8×C31 | C22 | semidirect |
| 11. C2×D248 | C22 | semidirect |
| 12. #11758414 | C22 | direct (N × H) |
| 13. C2×C31⋊C16 | C22 | semidirect |
| 22. D8×C31 | C23 | semidirect |
| 26. D248 | C23 | semidirect |
| 27. C31⋊C16 | C23 | semidirect |
| 44. C22×C31 | D16 | semidirect |
| 51. C22×D8 | D31 | semidirect |
| 55. C2×C31 | C2×D16 | semidirect |
| 63. C2×D8 | C2×D31 | semidirect |
| 67. C31 | C22×D16 | semidirect |
| 78. D8 | C22×D31 | semidirect |
| 99. C22 | #11758414 | direct (N × H) |
| 105. C2 | C2×#11758414 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D248 | 2 |
| C2×#11758414 | 2 |
| C22×C31⋊C16 | 2 |
| C22×D8×C31 | 2 |
| C22×D16 | 31 |