Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
424 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 121 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 |
|---|---|---|
| 2. C4×Q8×D31 | C2 | semidirect |
| 3. #14521361 | C2 | semidirect |
| 4. #14521345 | C2 | semidirect |
| 5. #14521344 | C2 | semidirect |
| 6. #14521246 | C2 | semidirect |
| 7. #14521186 | C2 | semidirect |
| 8. #14521150 | C2 | semidirect |
| 9. #14521146 | C2 | semidirect |
| 10. #14521105 | C2 | semidirect |
| 11. C31×#460 | C2 | semidirect |
| 86. Q8×C31 | #41 | semidirect |
| 113. Dic62 | #41 | semidirect |
| 142. #460 | D31 | semidirect |
| 183. C31 | #3112 | semidirect |
| 231. Q8 | #92497 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14521597 | 2 |
| C4×Q8×D31 | 2 |
| #14521361 | 2 |
| #14521345 | 2 |
| #14521344 | 2 |
| #14521246 | 2 |
| #14521186 | 2 |
| #14521150 | 2 |
| #14521146 | 2 |
| #14521105 | 2 |
| C31×#460 | 2 |
| #3112 | 31 |