Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
166 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 69 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 |
|---|---|---|
| 3. #14557283 | C2 | semidirect |
| 4. Q8⋊#64436 | C2 | semidirect |
| 6. #14557254 | C2 | semidirect |
| 7. C8×Q8×C37 | C2 | semidirect |
| 43. Q8×C37 | M16 | semidirect |
| 56. C8×C37 | SD16 | semidirect |
| 78. C8×Q8 | D37 | semidirect |
| 85. C37 | #1583 | semidirect |
| 121. Q8 | #10596929 | semidirect |
| 138. C8 | #10596941 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#10596941 | 2 |
| #14557612 | 2 |
| #14557283 | 2 |
| Q8⋊#64436 | 2 |
| #14557260 | 2 |
| #14557254 | 2 |
| C8×Q8×C37 | 2 |
| #1583 | 37 |