Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
416 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 416 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. C4⋊Q8×D31 | C2 | semidirect |
| 3. #14521344 | C2 | semidirect |
| 4. #14521340 | C2 | semidirect |
| 5. #14521336 | C2 | semidirect |
| 6. #14521332 | C2 | semidirect |
| 7. #14521328 | C2 | semidirect |
| 8. #14521090 | C2 | semidirect |
| 9. #14521071 | C2 | semidirect |
| 11. C31×#477 | C2 | semidirect |
| 46. #92499 | Q8 | semidirect |
| 86. Q8×C31 | C2×Q8 | semidirect |
| 100. D124 | C2×Q8 | semidirect |
| 136. #477 | D31 | semidirect |
| 180. C31 | #3079 | semidirect |
| 226. Q8 | Q8×D31 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4⋊Q8×D31 | 2 |
| C4×#92499 | 2 |
| #14521344 | 2 |
| #14521340 | 2 |
| #14521336 | 2 |
| #14521332 | 2 |
| #14521328 | 2 |
| #14521090 | 2 |
| #14521071 | 2 |
| #14521049 | 2 |
| C31×#477 | 2 |
| #3079 | 31 |