Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
226 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 226 conjugacy classes of subgroups — too many to draw. Only its 53 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×Q16×D31 | C2 | semidirect |
| 2. C2×#11758388 | C2 | semidirect |
| 3. C2×#11758416 | C2 | semidirect |
| 5. #14520852 | C2 | semidirect |
| 6. (C2×D31)⋊C16 | C2 | semidirect |
| 7. C31×#358 | C2 | semidirect |
| 33. Q16×C31 | D4 | semidirect |
| 40. Dic124 | D4 | semidirect |
| 75. C2×D31 | SD32 | semidirect |
| 87. #358 | D31 | semidirect |
| 109. C31 | #2185 | semidirect |
| 123. Q16 | D124 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×D31 | 2 |
| C2×#11758388 | 2 |
| C2×#11758416 | 2 |
| #14521286 | 2 |
| #14520852 | 2 |
| (C2×D31)⋊C16 | 2 |
| C31×#358 | 2 |
| #2185 | 31 |