Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
1296 conjugacy classes of subgroups; only the 565 normal subgroups are shown.
This group has 1296 conjugacy classes of subgroups — too many to draw. Only its 565 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. #14558159 | C2 | direct (N × H) |
| 2. C2×#11924515 | C2 | semidirect |
| 3. C2×#11924513 | C2 | semidirect |
| 6. C22×Dic74 | C22 | semidirect |
| 8. #11924515 | C22 | semidirect |
| 9. #11924513 | C22 | semidirect |
| 10. C2×C4⋊Dic37 | C22 | semidirect |
| 11. C2×#10596936 | C22 | semidirect |
| 20. C24×C37 | Q8 | semidirect |
| 31. C2×Dic74 | C23 | semidirect |
| 35. C4⋊Dic37 | C23 | semidirect |
| 36. #10596936 | C23 | semidirect |
| 43. C23×C37 | C2×Q8 | semidirect |
| 69. C2×C37 | #543 | semidirect |
| 77. C37 | C2×#543 | semidirect |
| 92. C24 | Dic74 | semidirect |
| 115. C23 | C2×Dic74 | semidirect |
| 140. C2 | #14558159 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14558159 | 2 |
| C2×#11924515 | 2 |
| C2×#11924513 | 2 |
| C22×C22⋊Dic37 | 2 |
| C22×C22⋊C4×C37 | 2 |
| C2×#543 | 37 |