Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
1008 conjugacy classes of subgroups; only the 309 normal subgroups are shown.
This group has 1008 conjugacy classes of subgroups — too many to draw. Only its 309 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×#10596934 | C2 | semidirect |
| 2. C2×#11924495 | C2 | semidirect |
| 3. #14557538 | C2 | direct (N × H) |
| 4. C2×#11924457 | C2 | semidirect |
| 7. C2×#10596934 | C22 | semidirect |
| 8. C22×#64436 | C22 | semidirect |
| 10. #11924495 | C22 | semidirect |
| 11. C2×C4⋊Dic37 | C22 | semidirect |
| 14. #11924457 | C22 | semidirect |
| 19. C22×D4×C37 | C4 | semidirect |
| 35. C2×D4×C37 | C2×C4 | semidirect |
| 46. C4⋊Dic37 | C23 | semidirect |
| 50. C2×#64436 | C23 | semidirect |
| 95. C2×C37 | #418 | semidirect |
| 103. C37 | C2×#418 | semidirect |
| 108. C22×D4 | Dic37 | semidirect |
| 133. C2×D4 | C2×Dic37 | semidirect |
| 192. C2 | #14557538 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#10596934 | 2 |
| C2×#11924495 | 2 |
| #14557538 | 2 |
| C2×#11924457 | 2 |
| C23×D4×C37 | 2 |
| C2×#418 | 37 |