Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
334 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 3. #14557542 | C2 | semidirect |
| 4. #14557440 | C2 | semidirect |
| 5. #14557301 | C2 | semidirect |
| 6. #14557294 | C2 | semidirect |
| 24. #137×C37 | C4 | semidirect |
| 37. C2×Q8×C37 | C2×C4 | semidirect |
| 50. M16×C37 | C2×C4 | semidirect |
| 132. C37 | #1882 | semidirect |
| 136. #137 | Dic37 | semidirect |
| 162. C2×Q8 | C2×Dic37 | semidirect |
| 177. M16 | C2×Dic37 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14558016 | 2 |
| C2×#11924463 | 2 |
| #14557542 | 2 |
| #14557440 | 2 |
| #14557301 | 2 |
| #14557294 | 2 |
| C2×#137×C37 | 2 |
| #1882 | 37 |