Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
336 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 123 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. #14521777 | C2 | semidirect |
| 4. #14521400 | C2 | semidirect |
| 5. #14521357 | C2 | semidirect |
| 8. #14521260 | C2 | semidirect |
| 9. C4×Dic124 | C2 | semidirect |
| 11. C8×Q8×C31 | C2 | semidirect |
| 120. C8×Q8 | D31 | semidirect |
| 156. C31 | #3364 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14521777 | 2 |
| #14521772 | 2 |
| #14521404 | 2 |
| #14521400 | 2 |
| #14521357 | 2 |
| #14521330 | 2 |
| #14521272 | 2 |
| #14521260 | 2 |
| C4×Dic124 | 2 |
| C4×#92470 | 2 |
| C8×Q8×C31 | 2 |
| #3364 | 31 |