Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
472 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 141 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×Q16×D31 | C2 | semidirect |
| 3. #14521427 | C2 | semidirect |
| 4. #14521290 | C2 | semidirect |
| 5. #14521287 | C2 | semidirect |
| 6. #14521257 | C2 | semidirect |
| 7. #14521205 | C2 | semidirect |
| 8. #14521203 | C2 | semidirect |
| 9. Q16×Dic31 | C2 | semidirect |
| 11. C22×Q16×C31 | C2 | semidirect |
| 57. Q16×C31 | D4 | semidirect |
| 94. C22⋊D31 | Q16 | direct (N × H) |
| 113. C22×C31 | C2×Q16 | semidirect |
| 117. C2×D31 | C2×Q16 | semidirect |
| 127. Dic31 | C2×Q16 | semidirect |
| 129. C22×Q16 | D31 | semidirect |
| 173. C31 | D4×Q16 | semidirect |
| 193. Q16 | C22⋊D31 | direct (N × H) |
| 248. C22 | Q16×D31 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×D31 | 2 |
| Q8×C22⋊D31 | 2 |
| #14521427 | 2 |
| #14521290 | 2 |
| #14521287 | 2 |
| #14521257 | 2 |
| #14521205 | 2 |
| #14521203 | 2 |
| Q16×Dic31 | 2 |
| C8×C22⋊D31 | 2 |
| C22×Q16×C31 | 2 |
| D4×Q16 | 31 |