Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
584 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 149 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×#11924564 | C2 | semidirect |
| 2. C2×#11924533 | C2 | semidirect |
| 3. C4×#10596962 | C2 | semidirect |
| 4. #14557734 | C2 | semidirect |
| 5. #14557729 | C2 | semidirect |
| 6. #14557539 | C2 | semidirect |
| 7. C37×#423 | C2 | semidirect |
| 12. C2×#10596930 | C22 | semidirect |
| 13. C2×D296 | C22 | semidirect |
| 17. C4×Dic74 | C22 | semidirect |
| 18. C4×D148 | C22 | semidirect |
| 23. #11924458 | C22 | semidirect |
| 26. C4⋊C8×C37 | C22 | semidirect |
| 32. #10596962 | D4 | semidirect |
| 78. D148 | C2×D4 | semidirect |
| 82. Dic74 | C2×D4 | semidirect |
| 94. C4×C37 | AGL(1,ℤ/8) | semidirect |
| 110. #423 | D37 | semidirect |
| 112. C37 | #3038 | semidirect |
| 130. C4⋊C8 | C2×D37 | semidirect |
| 201. C4 | #11924564 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11924564 | 2 |
| C2×#11924533 | 2 |
| C4×#10596962 | 2 |
| #14557734 | 2 |
| #14557729 | 2 |
| #14557539 | 2 |
| C37×#423 | 2 |
| #3038 | 37 |