Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
476 conjugacy classes of subgroups; only the 200 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 200 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. #14558544 | C2 | semidirect |
| 3. #14558543 | C2 | semidirect |
| 4. C2×#11924605 | C2 | semidirect |
| 15. #11924544 | C4 | semidirect |
| 16. #11924543 | C4 | semidirect |
| 17. #11924542 | C4 | semidirect |
| 20. #131×C37 | C4 | semidirect |
| 34. M16×C37 | C2×C4 | semidirect |
| 35. C2×C8×C37 | C2×C4 | semidirect |
| 36. #10596934 | C2×C4 | semidirect |
| 37. C2×#64436 | C2×C4 | semidirect |
| 38. #10596929 | C2×C4 | semidirect |
| 39. C8×D37 | C2×C4 | semidirect |
| 40. C8×D37 | C2×C4 | semidirect |
| 84. C37 | #2913 | semidirect |
| 89. #131 | #3866 | semidirect |
| 110. M16 | C2×#3866 | semidirect |
| 116. C2×C8 | C2×#3866 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14558602 | 2 |
| #14558544 | 2 |
| #14558543 | 2 |
| C2×#11924605 | 2 |
| #131×D37 | 2 |
| #2913 | 37 |