Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
552 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 221 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×#10596929 | C2 | semidirect |
| 3. #14557612 | C2 | direct (N × H) |
| 4. C2×C4⋊#64436 | C2 | semidirect |
| 5. C2×#11924448 | C2 | semidirect |
| 6. C2×C4×C8×C37 | C2 | semidirect |
| 10. C2×#10596929 | C22 | semidirect |
| 16. C4⋊#64436 | C22 | semidirect |
| 17. #11924448 | C22 | semidirect |
| 21. C4×C8×C37 | C22 | semidirect |
| 34. C2×C8×C37 | D4 | semidirect |
| 50. C2×C4×C37 | M16 | semidirect |
| 64. C8×C37 | C2×D4 | semidirect |
| 76. C4×C37 | C2×M16 | semidirect |
| 81. C2×C37 | #436 | semidirect |
| 91. C2×C4×C8 | D37 | semidirect |
| 92. C37 | C2×#436 | semidirect |
| 107. C4×C8 | C2×D37 | semidirect |
| 123. C2×C8 | D148 | semidirect |
| 142. C2×C4 | #10596929 | semidirect |
| 151. C8 | C2×D148 | semidirect |
| 163. C4 | C2×#10596929 | semidirect |
| 167. C2 | #14557612 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#10596929 | 2 |
| C2×C4×D148 | 2 |
| #14557612 | 2 |
| C2×C4⋊#64436 | 2 |
| C2×#11924448 | 2 |
| C2×C4×C8×C37 | 2 |
| C2×#436 | 37 |