Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
420 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 420 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. Q8×D148 | C2 | semidirect |
| 3. #14557885 | C2 | semidirect |
| 4. #14557865 | C2 | semidirect |
| 5. #14557763 | C2 | semidirect |
| 6. #14557739 | C2 | semidirect |
| 7. #14557673 | C2 | semidirect |
| 8. C4×#10596941 | C2 | semidirect |
| 9. #14557598 | C2 | semidirect |
| 10. #103×D37 | C2 | semidirect |
| 11. C37×#475 | C2 | semidirect |
| 81. Q8×C37 | #41 | semidirect |
| 94. D148 | SD16 | semidirect |
| 133. #475 | D37 | semidirect |
| 140. C37 | #3298 | semidirect |
| 213. Q8 | #10596966 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D148 | 2 |
| #14558186 | 2 |
| #14557885 | 2 |
| #14557865 | 2 |
| #14557763 | 2 |
| #14557739 | 2 |
| #14557673 | 2 |
| C4×#10596941 | 2 |
| #14557598 | 2 |
| #103×D37 | 2 |
| C37×#475 | 2 |
| #3298 | 37 |