Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
472 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 472 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. C22×Dic124 | C2 | semidirect |
| 2. C2×Q16×D31 | C2 | semidirect |
| 4. #14521427 | C2 | semidirect |
| 5. #14521291 | C2 | semidirect |
| 6. #14521258 | C2 | semidirect |
| 7. #14521206 | C2 | semidirect |
| 8. #14521204 | C2 | semidirect |
| 9. #14521143 | C2 | semidirect |
| 11. C31×#467 | C2 | semidirect |
| 78. Dic124 | D4 | semidirect |
| 90. C22⋊D31 | Q16 | semidirect |
| 113. C22×C31 | C2×Q16 | semidirect |
| 117. C2×D31 | C2×Q16 | semidirect |
| 127. Dic31 | C2×Q16 | semidirect |
| 133. #467 | D31 | semidirect |
| 173. C31 | D4×Q16 | semidirect |
| 248. C22 | Q16×D31 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic124 | 2 |
| C2×Q16×D31 | 2 |
| #14521712 | 2 |
| #14521427 | 2 |
| #14521291 | 2 |
| #14521258 | 2 |
| #14521206 | 2 |
| #14521204 | 2 |
| #14521143 | 2 |
| C8×C22⋊D31 | 2 |
| C31×#467 | 2 |
| D4×Q16 | 31 |