Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
376 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 133 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. #14558161 | C2 | semidirect |
| 3. #14557843 | C2 | semidirect |
| 4. #14557832 | C2 | semidirect |
| 5. #14557827 | C2 | semidirect |
| 6. #14557812 | C2 | semidirect |
| 7. C2×#11924469 | C2 | semidirect |
| 8. #14557561 | C2 | semidirect |
| 11. C37×#428 | C2 | semidirect |
| 46. #10596962 | Q8 | semidirect |
| 130. #428 | D37 | semidirect |
| 135. C37 | #3083 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14558161 | 2 |
| #14558014 | 2 |
| #14557843 | 2 |
| #14557832 | 2 |
| #14557827 | 2 |
| #14557812 | 2 |
| C2×#11924469 | 2 |
| #14557561 | 2 |
| #14557535 | 2 |
| #14557527 | 2 |
| C37×#428 | 2 |
| #3083 | 37 |