Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
416 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 137 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×#11924535 | C2 | semidirect |
| 3. #14557827 | C2 | semidirect |
| 4. #14557822 | C2 | semidirect |
| 5. #14557817 | C2 | semidirect |
| 6. #14557812 | C2 | semidirect |
| 7. #14557576 | C2 | semidirect |
| 8. #14557556 | C2 | semidirect |
| 11. C37×#428 | C2 | semidirect |
| 50. #10596962 | Q8 | semidirect |
| 104. D148 | C2×Q8 | semidirect |
| 111. Dic74 | C2×Q8 | semidirect |
| 146. #428 | D37 | semidirect |
| 150. C37 | #3079 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11924535 | 2 |
| #14558001 | 2 |
| #14557827 | 2 |
| #14557822 | 2 |
| #14557817 | 2 |
| #14557812 | 2 |
| #14557576 | 2 |
| #14557556 | 2 |
| #14557535 | 2 |
| #14557532 | 2 |
| C37×#428 | 2 |
| #3079 | 37 |