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×#11758496 | C2 | semidirect |
| 2. #14521721 | C2 | semidirect |
| 3. #14521702 | C2 | semidirect |
| 4. #14521423 | C2 | semidirect |
| 5. #14521281 | C2 | semidirect |
| 6. #14521245 | C2 | semidirect |
| 7. #14521210 | C2 | semidirect |
| 8. #14521197 | C2 | semidirect |
| 9. C4×#92481 | C2 | semidirect |
| 10. #14521114 | C2 | semidirect |
| 11. C31×#462 | C2 | semidirect |
| 70. #92481 | D4 | semidirect |
| 130. C4×C31 | #135 | semidirect |
| 140. #462 | D31 | semidirect |
| 182. C31 | #3284 | semidirect |
| 272. C4 | #11758496 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11758496 | 2 |
| #14521721 | 2 |
| #14521702 | 2 |
| #14521423 | 2 |
| #14521281 | 2 |
| #14521245 | 2 |
| #14521210 | 2 |
| #14521197 | 2 |
| C4×#92481 | 2 |
| #14521114 | 2 |
| C31×#462 | 2 |
| #3284 | 31 |