Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
224 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 85 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. C22×#10596925 | C2 | semidirect |
| 3. #14557339 | C2 | direct (N × H) |
| 4. C2×#108×C37 | C2 | semidirect |
| 15. C2×#10596925 | C22 | semidirect |
| 19. #108×C37 | C22 | semidirect |
| 81. C2×C37 | #359 | semidirect |
| 86. C2×#108 | D37 | semidirect |
| 88. C37 | C2×#359 | semidirect |
| 103. #108 | C2×D37 | semidirect |
| 165. C2 | #14557339 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11924558 | 2 |
| C22×#10596925 | 2 |
| #14557339 | 2 |
| C2×#108×C37 | 2 |
| C2×#359 | 37 |