Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
426 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 139 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. Q8×D124 | C2 | semidirect |
| 2. #14521395 | C2 | semidirect |
| 3. #14521329 | C2 | semidirect |
| 4. #14521241 | C2 | semidirect |
| 5. Q8×C31⋊C8 | C2 | semidirect |
| 6. C4×#92479 | C2 | semidirect |
| 7. C31×#550 | C2 | semidirect |
| 46. Q8×C31 | D8 | semidirect |
| 58. D124 | #41 | semidirect |
| 77. #550 | D31 | semidirect |
| 105. C31 | #3358 | semidirect |
| 129. Q8 | #92479 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D124 | 2 |
| #14521395 | 2 |
| #14521329 | 2 |
| #14521241 | 2 |
| Q8×C31⋊C8 | 2 |
| C4×#92479 | 2 |
| C31×#550 | 2 |
| #3358 | 31 |