Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
472 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 472 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×Dic124 | C2 | semidirect |
| 3. #14521429 | C2 | semidirect |
| 4. #14521290 | C2 | semidirect |
| 5. #14521260 | C2 | semidirect |
| 6. #14521207 | C2 | semidirect |
| 7. C4×Dic124 | C2 | semidirect |
| 54. Dic124 | D4 | direct (N × H) |
| 56. D4×C31 | Q16 | semidirect |
| 78. C22×C31 | C2×Q16 | semidirect |
| 82. C4×C31 | C2×Q16 | semidirect |
| 120. C31 | D4×Q16 | semidirect |
| 153. D4 | Dic124 | direct (N × H) |
| 169. C22 | C2×Dic124 | semidirect |
| 176. C4 | C2×Dic124 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic124 | 2 |
| D4×Dic62 | 2 |
| #14521429 | 2 |
| #14521290 | 2 |
| #14521260 | 2 |
| #14521207 | 2 |
| C4×Dic124 | 2 |
| C8×D4×C31 | 2 |
| D4×Q16 | 31 |