Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
370 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 370 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. #14521778 | C2 | semidirect |
| 3. #14521400 | C2 | semidirect |
| 4. #14521335 | C2 | semidirect |
| 7. C8×Q8×C31 | C2 | semidirect |
| 44. Q8×C31 | SD16 | semidirect |
| 76. C8×Q8 | D31 | semidirect |
| 98. C31 | #3359 | semidirect |
| 122. Q8 | #92470 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14521778 | 2 |
| Q8×D124 | 2 |
| #14521400 | 2 |
| #14521335 | 2 |
| #14521255 | 2 |
| C4×#92470 | 2 |
| C8×Q8×C31 | 2 |
| #3359 | 31 |