Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
382 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 382 conjugacy classes of subgroups — too many to draw. Only its 125 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. #14521415 | C2 | semidirect |
| 3. #14521397 | C2 | semidirect |
| 4. #14521346 | C2 | semidirect |
| 5. #14521326 | C2 | semidirect |
| 6. #14521249 | C2 | semidirect |
| 7. #14521249 | C2 | semidirect |
| 8. #14521180 | C2 | semidirect |
| 9. #14521147 | C2 | semidirect |
| 10. C4×#92481 | C2 | semidirect |
| 11. C31×#557 | C2 | semidirect |
| 79. Q8×C31 | #41 | semidirect |
| 120. #557 | D31 | semidirect |
| 165. C31 | #3368 | semidirect |
| 204. Q8 | #92499 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14521721 | 2 |
| #14521415 | 2 |
| #14521397 | 2 |
| #14521346 | 2 |
| #14521326 | 2 |
| #14521249 | 2 |
| #14521180 | 2 |
| #14521147 | 2 |
| C4×#92481 | 2 |
| C31×#557 | 2 |
| #3368 | 31 |