Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
386 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 117 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. #14521765 | C2 | semidirect |
| 2. #14521702 | C2 | semidirect |
| 3. #14521375 | C2 | semidirect |
| 4. #14521369 | C2 | semidirect |
| 5. #14521336 | C2 | semidirect |
| 6. #14521326 | C2 | semidirect |
| 7. #14521303 | C2 | semidirect |
| 8. C4×D248 | C2 | semidirect |
| 9. #14521128 | C2 | semidirect |
| 10. #14521088 | C2 | semidirect |
| 11. C31×#498 | C2 | semidirect |
| 100. C8×C31 | #41 | semidirect |
| 124. #498 | D31 | semidirect |
| 168. C31 | #3354 | semidirect |
| 229. C8 | #92499 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14521765 | 2 |
| #14521702 | 2 |
| #14521375 | 2 |
| #14521369 | 2 |
| #14521336 | 2 |
| #14521326 | 2 |
| #14521303 | 2 |
| C4×D248 | 2 |
| #14521128 | 2 |
| #14521088 | 2 |
| C31×#498 | 2 |
| #3354 | 31 |