Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
564 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 157 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×C4×D148 | C2 | semidirect |
| 4. #14557745 | C2 | direct (N × H) |
| 5. C2×C4⋊#64436 | C2 | semidirect |
| 6. C2×#11924460 | C2 | semidirect |
| 7. C2×#11924457 | C2 | semidirect |
| 8. C2×#124×C37 | C2 | semidirect |
| 12. C2×#10596941 | C22 | semidirect |
| 18. C4×D148 | C22 | semidirect |
| 21. C4⋊#64436 | C22 | semidirect |
| 22. #11924460 | C22 | semidirect |
| 23. #11924457 | C22 | semidirect |
| 27. #124×C37 | C22 | semidirect |
| 119. C2×C37 | #463 | semidirect |
| 126. C2×#124 | D37 | semidirect |
| 132. C37 | C2×#463 | semidirect |
| 144. #124 | C2×D37 | semidirect |
| 243. C2 | #14557745 | 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 |
| C22×#10596939 | 2 |
| C2×C4×D148 | 2 |
| #14557745 | 2 |
| C2×C4⋊#64436 | 2 |
| C2×#11924460 | 2 |
| C2×#11924457 | 2 |
| C2×#124×C37 | 2 |
| C2×#463 | 37 |