Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
766 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 766 conjugacy classes of subgroups — too many to draw. Only its 161 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. #14558040 | C2 | semidirect |
| 2. #14557723 | C2 | semidirect |
| 3. #14557720 | C2 | semidirect |
| 4. #14557507 | C2 | semidirect |
| 5. C37×#585 | C2 | semidirect |
| 6. C22×C4×D37 | C22 | semidirect |
| 7. #11924517 | C22 | semidirect |
| 10. #11924504 | C22 | semidirect |
| 12. #11924495 | C22 | semidirect |
| 13. #11924451 | C22 | semidirect |
| 26. C2×Q8×C37 | D4 | semidirect |
| 29. C2×D4×C37 | D4 | semidirect |
| 32. C22×C4×C37 | D4 | semidirect |
| 83. #585 | D37 | semidirect |
| 88. C37 | #3025 | semidirect |
| 109. C2×Q8 | C22⋊D37 | semidirect |
| 113. C2×D4 | C22⋊D37 | semidirect |
| 119. C22×C4 | C22⋊D37 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14558040 | 2 |
| #14557723 | 2 |
| #14557720 | 2 |
| #14557507 | 2 |
| C37×#585 | 2 |
| #3025 | 37 |