Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
416 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 416 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. C2×#11758446 | C2 | semidirect |
| 3. #14521345 | C2 | semidirect |
| 4. #14521340 | C2 | semidirect |
| 5. #14521335 | C2 | semidirect |
| 6. #14521330 | C2 | semidirect |
| 7. #14521091 | C2 | semidirect |
| 9. C31×#423 | C2 | semidirect |
| 41. #92495 | Q8 | semidirect |
| 89. D124 | C2×Q8 | semidirect |
| 96. Dic62 | C2×Q8 | semidirect |
| 124. #423 | D31 | semidirect |
| 156. C31 | #3079 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11758446 | 2 |
| C4×#92495 | 2 |
| #14521345 | 2 |
| #14521340 | 2 |
| #14521335 | 2 |
| #14521330 | 2 |
| #14521091 | 2 |
| #14521051 | 2 |
| C31×#423 | 2 |
| #3079 | 31 |