Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
778 conjugacy classes of subgroups; only the 293 normal subgroups are shown.
This group has 778 conjugacy classes of subgroups — too many to draw. Only its 293 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. C2×#11924543 | C2 | semidirect |
| 2. #14558016 | C2 | semidirect |
| 3. #14557538 | C2 | semidirect |
| 4. #14557534 | C2 | semidirect |
| 5. #14557529 | C2 | semidirect |
| 6. C2×#11924457 | C2 | semidirect |
| 9. C2×#10596934 | C22 | semidirect |
| 10. C22×#64436 | C22 | semidirect |
| 13. #11924495 | C22 | semidirect |
| 14. C2×C4⋊Dic37 | C22 | semidirect |
| 15. #11924460 | C22 | semidirect |
| 16. #11924460 | C22 | semidirect |
| 17. #11924457 | C22 | semidirect |
| 18. #11924457 | C22 | semidirect |
| 19. #11924457 | C22 | semidirect |
| 21. H(5,𝔽2)×C37 | C4 | semidirect |
| 31. #41×C37 | C2×C4 | semidirect |
| 39. C2×D4×C37 | C2×C4 | semidirect |
| 105. C37 | #2897 | semidirect |
| 107. H(5,𝔽2) | Dic37 | semidirect |
| 129. #41 | C2×Dic37 | semidirect |
| 137. C2×D4 | C2×Dic37 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11924543 | 2 |
| #14558016 | 2 |
| #14557538 | 2 |
| #14557534 | 2 |
| #14557529 | 2 |
| C2×#11924457 | 2 |
| C2×H(5,𝔽2)×C37 | 2 |
| #2897 | 37 |