Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
152 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 67 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 |
|---|---|---|
| 4. #14557357 | C2 | semidirect |
| 5. #14557356 | C2 | semidirect |
| 6. #14557355 | C2 | semidirect |
| 7. C37×#365 | C2 | semidirect |
| 12. #11924475 | C4 | semidirect |
| 13. C16×D37 | C4 | semidirect |
| 36. C16×C37 | C2×C4 | semidirect |
| 37. #10596925 | C2×C4 | semidirect |
| 68. D37 | #365 | direct (N × H) |
| 75. #365 | D37 | direct (N × H) |
| 76. C37 | C2×#365 | semidirect |
| 106. C16 | C4×D37 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| M32×D37 | 2 |
| #108×D37 | 2 |
| #106×D37 | 2 |
| #14557357 | 2 |
| #14557356 | 2 |
| #14557355 | 2 |
| C37×#365 | 2 |
| C2×#365 | 37 |