Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
584 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 165 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. C22×#10596941 | C2 | semidirect |
| 3. C2×Q8×Dic37 | C2 | semidirect |
| 4. #14557731 | C2 | direct (N × H) |
| 5. C2×#11924465 | C2 | semidirect |
| 6. C2×#11924458 | C2 | semidirect |
| 7. C2×#11924457 | C2 | semidirect |
| 8. C22×SD16×C37 | C2 | semidirect |
| 13. C2×#10596941 | C22 | semidirect |
| 18. Q8×Dic37 | C22 | semidirect |
| 23. #11924465 | C22 | semidirect |
| 24. #11924458 | C22 | semidirect |
| 25. #11924457 | C22 | semidirect |
| 29. C2×SD16×C37 | C22 | semidirect |
| 35. C2×Q8×C37 | D4 | semidirect |
| 77. Q8×C37 | C2×D4 | semidirect |
| 92. C2×Dic37 | SD16 | semidirect |
| 118. Dic37 | C2×SD16 | semidirect |
| 121. C2×C37 | #460 | semidirect |
| 127. C22×SD16 | D37 | semidirect |
| 134. C37 | C2×#460 | semidirect |
| 143. C2×SD16 | C2×D37 | semidirect |
| 161. C2×Q8 | C22⋊D37 | semidirect |
| 203. Q8 | C2×C22⋊D37 | semidirect |
| 247. C2 | #14557731 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#10596941 | 2 |
| C2×#11924532 | 2 |
| C2×Q8×Dic37 | 2 |
| #14557731 | 2 |
| C2×#11924465 | 2 |
| C2×#11924458 | 2 |
| C2×#11924457 | 2 |
| C22×SD16×C37 | 2 |
| C2×#460 | 37 |