Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
494 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 494 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 |
|---|---|---|
| 1. C2×#11758493 | C2 | semidirect |
| 2. #14521719 | C2 | semidirect |
| 3. #14521702 | C2 | semidirect |
| 4. #14521275 | C2 | semidirect |
| 5. #14521256 | C2 | semidirect |
| 6. #14521241 | C2 | semidirect |
| 7. #14521208 | C2 | semidirect |
| 8. #14521193 | C2 | semidirect |
| 9. C4×#92470 | C2 | semidirect |
| 10. C8×D124 | C2 | semidirect |
| 11. C31×#492 | C2 | semidirect |
| 80. #92470 | D4 | semidirect |
| 128. C4×C31 | #135 | semidirect |
| 138. #492 | D31 | semidirect |
| 182. C31 | #3284 | semidirect |
| 272. C4 | #11758493 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11758493 | 2 |
| #14521719 | 2 |
| #14521702 | 2 |
| #14521275 | 2 |
| #14521256 | 2 |
| #14521241 | 2 |
| #14521208 | 2 |
| #14521193 | 2 |
| C4×#92470 | 2 |
| C8×D124 | 2 |
| C31×#492 | 2 |
| #3284 | 31 |