Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
420 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 141 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 |
|---|---|---|
| 2. #14557883 | C2 | semidirect |
| 3. #14557861 | C2 | semidirect |
| 4. #14557818 | C2 | semidirect |
| 5. #14557764 | C2 | semidirect |
| 6. #14557735 | C2 | semidirect |
| 7. #14557672 | C2 | semidirect |
| 8. C4×#10596941 | C2 | semidirect |
| 9. D4×#64436 | C2 | semidirect |
| 10. C2×#11924460 | C2 | semidirect |
| 11. D4×Q8×C37 | C2 | semidirect |
| 83. Q8×C37 | #41 | semidirect |
| 84. D4×C37 | SD16 | semidirect |
| 129. D4×Q8 | D37 | semidirect |
| 140. C37 | #3298 | semidirect |
| 213. Q8 | #10596964 | semidirect |
| 217. D4 | #10596941 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14558187 | 2 |
| #14557883 | 2 |
| #14557861 | 2 |
| #14557818 | 2 |
| #14557764 | 2 |
| #14557735 | 2 |
| #14557672 | 2 |
| C4×#10596941 | 2 |
| D4×#64436 | 2 |
| C2×#11924460 | 2 |
| D4×Q8×C37 | 2 |
| #3298 | 37 |