Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
596 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 596 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×D296 | C2 | semidirect |
| 2. C22×#10596929 | C2 | semidirect |
| 3. C2×#11924511 | C2 | semidirect |
| 4. #14557787 | C2 | direct (N × H) |
| 5. C2×#11924456 | C2 | semidirect |
| 6. C2×#106×C37 | C2 | semidirect |
| 11. C2×D296 | C22 | semidirect |
| 13. C2×#10596929 | C22 | semidirect |
| 16. #11924511 | C22 | semidirect |
| 18. #11924456 | C22 | semidirect |
| 21. #106×C37 | C22 | semidirect |
| 37. C2×C8×C37 | D4 | semidirect |
| 69. C8×C37 | C2×D4 | semidirect |
| 87. C2×C37 | #469 | semidirect |
| 96. C2×#106 | D37 | semidirect |
| 98. C37 | C2×#469 | semidirect |
| 112. #106 | C2×D37 | semidirect |
| 133. C2×C8 | D148 | semidirect |
| 162. C8 | C2×D148 | semidirect |
| 180. C2 | #14557787 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D296 | 2 |
| C22×#10596929 | 2 |
| C2×#11924511 | 2 |
| #14557787 | 2 |
| C2×#11924456 | 2 |
| C2×#106×C37 | 2 |
| C2×#469 | 37 |