Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
424 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 181 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. #14557937 | C2 | direct (N × H) |
| 27. C2×C8×C37 | Q8 | semidirect |
| 36. C2×#64436 | Q8 | semidirect |
| 52. C8×C37 | C2×Q8 | semidirect |
| 53. #64436 | C2×Q8 | semidirect |
| 66. C2×C37 | #500 | semidirect |
| 76. C37 | C2×#500 | semidirect |
| 99. C2×C8 | Dic74 | semidirect |
| 123. C8 | C2×Dic74 | semidirect |
| 135. C2 | #14557937 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11924535 | 2 |
| #14557937 | 2 |
| C2×#11924470 | 2 |
| C2×#11924469 | 2 |
| C2×C8×Dic37 | 2 |
| C2×#107×C37 | 2 |
| C2×#500 | 37 |