Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
372 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 372 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. #14521772 | C2 | semidirect |
| 2. Q8×D124 | C2 | semidirect |
| 3. #14521409 | C2 | semidirect |
| 4. #14521400 | C2 | semidirect |
| 5. #14521345 | C2 | semidirect |
| 6. #14521330 | C2 | semidirect |
| 8. #14521255 | C2 | semidirect |
| 9. #14521151 | C2 | semidirect |
| 11. C31×#446 | C2 | semidirect |
| 126. #446 | D31 | semidirect |
| 163. C31 | #3367 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14521772 | 2 |
| Q8×D124 | 2 |
| #14521409 | 2 |
| #14521400 | 2 |
| #14521345 | 2 |
| #14521330 | 2 |
| #14521265 | 2 |
| #14521255 | 2 |
| #14521151 | 2 |
| C4×D248 | 2 |
| C31×#446 | 2 |
| #3367 | 31 |