Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
166 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 56 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. #14558584 | C2 | semidirect |
| 3. #14558395 | C2 | semidirect |
| 4. Q8⋊#64438 | C2 | semidirect |
| 6. C8×#64438 | C2 | semidirect |
| 58. #64438 | SD16 | semidirect |
| 60. #64436 | M16 | semidirect |
| 85. C37 | #1590 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14558584 | 2 |
| #14558567 | 2 |
| #14558395 | 2 |
| Q8⋊#64438 | 2 |
| #14558381 | 2 |
| C8×#64438 | 2 |
| #14557618 | 2 |
| #1590 | 37 |