Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
512 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 165 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 |
|---|---|---|
| 3. #14521287 | C2 | direct (N × H) |
| 4. C2×#11758406 | C2 | semidirect |
| 5. C2×#11758423 | C2 | semidirect |
| 6. C22×Q16×C31 | C2 | semidirect |
| 10. C2×Q16×C31 | C22 | semidirect |
| 20. #11758423 | C22 | semidirect |
| 21. #11758406 | C22 | semidirect |
| 48. C22×D31 | Q16 | semidirect |
| 76. C2×D31 | C2×Q16 | semidirect |
| 83. C22×Q16 | D31 | semidirect |
| 89. C2×C31 | #467 | semidirect |
| 97. C2×Q16 | C2×D31 | semidirect |
| 109. C31 | C2×#467 | semidirect |
| 171. C2 | #14521287 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C8×D31 | 2 |
| C2×#11758523 | 2 |
| #14521287 | 2 |
| C2×#11758406 | 2 |
| C2×#11758423 | 2 |
| C22×Q16×C31 | 2 |
| C2×#467 | 31 |