Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
564 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 564 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×#11924558 | C2 | semidirect |
| 2. C2×#11924556 | C2 | semidirect |
| 3. #14558079 | C2 | semidirect |
| 4. #14557926 | C2 | semidirect |
| 5. #14557924 | C2 | semidirect |
| 6. #14557921 | C2 | semidirect |
| 7. #14557919 | C2 | semidirect |
| 8. C2×#11924446 | C2 | semidirect |
| 9. C2×#135×C37 | C2 | semidirect |
| 54. C2×C8×C37 | D4 | semidirect |
| 66. C2×#64436 | D4 | semidirect |
| 119. C2×#135 | D37 | semidirect |
| 126. C37 | #3150 | semidirect |
| 180. C2×C8 | C22⋊D37 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11924558 | 2 |
| C2×#11924556 | 2 |
| #14558079 | 2 |
| #14557926 | 2 |
| #14557924 | 2 |
| #14557921 | 2 |
| #14557919 | 2 |
| C2×#11924446 | 2 |
| C2×#135×C37 | 2 |
| #3150 | 37 |