Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
1008 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 1008 conjugacy classes of subgroups — too many to draw. Only its 269 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×#10596934 | C2 | semidirect |
| 3. #14557537 | C2 | direct (N × H) |
| 4. C2×#11924456 | C2 | semidirect |
| 5. C2×#117×C37 | C2 | semidirect |
| 10. C22×D148 | C4 | semidirect |
| 14. C2×#10596934 | C22 | semidirect |
| 15. C22×#64436 | C22 | semidirect |
| 16. #11924456 | C22 | semidirect |
| 19. #117×C37 | C22 | semidirect |
| 20. C2×C4⋊C4×C37 | C22 | semidirect |
| 42. C2×D148 | C2×C4 | semidirect |
| 45. C4⋊C4×C37 | C23 | semidirect |
| 50. C2×#64436 | C23 | semidirect |
| 94. C2×C37 | #418 | semidirect |
| 100. C2×#117 | D37 | semidirect |
| 103. C37 | C2×#418 | semidirect |
| 116. #117 | C2×D37 | semidirect |
| 117. C2×C4⋊C4 | C2×D37 | semidirect |
| 146. C4⋊C4 | C22×D37 | semidirect |
| 192. C2 | #14557537 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D148 | 2 |
| C22×#10596934 | 2 |
| #14557537 | 2 |
| C2×#11924456 | 2 |
| C2×#117×C37 | 2 |
| C2×#418 | 37 |