Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
1504 conjugacy classes of subgroups; only the 770 normal subgroups are shown.
This group has 1504 conjugacy classes of subgroups — too many to draw. Only its 770 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. C2×#11924623 | C2 | direct (N × H) |
| 2. C22×#10596953 | C2 | semidirect |
| 3. C22×#10596957 | C2 | semidirect |
| 4. C22×D37⋊C8 | C2 | semidirect |
| 5. C23×#64438 | C2 | semidirect |
| 7. #11924623 | C22 | direct (N × H) |
| 8. C2×#10596953 | C22 | semidirect |
| 9. C2×#10596957 | C22 | semidirect |
| 10. C2×D37⋊C8 | C22 | semidirect |
| 14. C22×#64438 | C22 | semidirect |
| 36. #10596957 | C23 | semidirect |
| 40. C2×#64438 | C23 | semidirect |
| 41. #10596953 | C23 | semidirect |
| 42. D37⋊C8 | C23 | semidirect |
| 63. C22×C37 | #131 | semidirect |
| 74. C2×C37 | C2×#131 | semidirect |
| 83. C37 | C22×#131 | semidirect |
| 142. C22 | #11924623 | direct (N × H) |
| 151. C2 | C2×#11924623 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11924623 | 2 |
| C22×#10596953 | 2 |
| C22×#10596957 | 2 |
| C22×D37⋊C8 | 2 |
| C23×#64438 | 2 |
| C22×#10596964 | 2 |
| C22×#131 | 37 |