Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
494 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 133 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. #14521721 | C2 | semidirect |
| 3. #14521703 | C2 | semidirect |
| 4. #14521422 | C2 | semidirect |
| 5. #14521279 | C2 | semidirect |
| 6. #14521259 | C2 | semidirect |
| 7. #14521244 | C2 | semidirect |
| 8. #14521214 | C2 | semidirect |
| 9. #14521195 | C2 | semidirect |
| 10. C8×D124 | C2 | semidirect |
| 11. C4×SD16×C31 | C2 | semidirect |
| 60. SD16×C31 | D4 | semidirect |
| 130. C4×C31 | #135 | semidirect |
| 144. C4×SD16 | D31 | semidirect |
| 182. C31 | #3284 | semidirect |
| 204. SD16 | D124 | 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 |
| #14521721 | 2 |
| #14521703 | 2 |
| #14521422 | 2 |
| #14521279 | 2 |
| #14521259 | 2 |
| #14521244 | 2 |
| #14521214 | 2 |
| #14521195 | 2 |
| C8×D124 | 2 |
| C4×SD16×C31 | 2 |
| #3284 | 31 |