Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
656 conjugacy classes of subgroups; only the 322 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 322 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 |
|---|---|---|
| 2. C4×#10596953 | C2 | direct (N × H) |
| 3. C2×#11924591 | C2 | semidirect |
| 4. C2×C4×#64438 | C2 | semidirect |
| 6. C2×#10596953 | C4 | direct (N × H) |
| 9. #11924591 | C22 | semidirect |
| 10. C4×#64438 | C22 | semidirect |
| 34. C2×#64438 | C2×C4 | semidirect |
| 36. #10596953 | C2×C4 | direct (N × H) |
| 50. C2×C4×C37 | M16 | semidirect |
| 55. C2×Dic37 | M16 | semidirect |
| 65. #64438 | C22×C4 | semidirect |
| 76. C4×C37 | C2×M16 | semidirect |
| 79. Dic37 | C2×M16 | semidirect |
| 82. C2×C37 | C4×M16 | semidirect |
| 92. C37 | C2×C4×M16 | semidirect |
| 147. C2×C4 | #10596953 | direct (N × H) |
| 167. C4 | C2×#10596953 | direct (N × H) |
| 169. C2 | C4×#10596953 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#10596953 | 2 |
| C4×#10596953 | 2 |
| C2×#11924591 | 2 |
| C2×C4×#64438 | 2 |
| C2×C42×D37 | 2 |
| C2×C4×M16 | 37 |