Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
656 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 157 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×#11924561 | C2 | semidirect |
| 2. C2×#11924533 | C2 | semidirect |
| 3. #14557923 | C2 | semidirect |
| 4. #14557909 | C2 | semidirect |
| 5. #14557907 | C2 | semidirect |
| 6. C4×#10596934 | C2 | semidirect |
| 7. C37×#532 | C2 | semidirect |
| 11. C2×#10596941 | C22 | semidirect |
| 12. C2×#10596939 | C22 | semidirect |
| 17. #11924447 | C22 | semidirect |
| 18. C4×#64436 | C22 | semidirect |
| 20. C4⋊Q8×C37 | C22 | semidirect |
| 21. #127×C37 | C22 | semidirect |
| 22. #124×C37 | C22 | semidirect |
| 48. #10596934 | D4 | semidirect |
| 71. #64436 | C2×D4 | semidirect |
| 83. C4×C37 | AGL(1,ℤ/8) | semidirect |
| 92. #532 | D37 | semidirect |
| 98. C37 | #3151 | semidirect |
| 106. C4⋊Q8 | C2×D37 | semidirect |
| 110. #127 | C2×D37 | semidirect |
| 111. #124 | C2×D37 | semidirect |
| 174. C4 | #11924561 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11924561 | 2 |
| C2×#11924533 | 2 |
| #14557923 | 2 |
| #14557909 | 2 |
| #14557907 | 2 |
| C4×#10596934 | 2 |
| C37×#532 | 2 |
| #3151 | 37 |