Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
188 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 61 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 |
|---|---|---|
| 2. #14557733 | C2 | semidirect |
| 3. #14557286 | C2 | semidirect |
| 4. #14557276 | C2 | semidirect |
| 5. C8×Q8×C37 | C2 | semidirect |
| 34. Q8×C37 | D8 | semidirect |
| 47. C8×C37 | SD16 | semidirect |
| 67. C8×Q8 | D37 | semidirect |
| 70. C37 | #1668 | semidirect |
| 99. Q8 | D296 | semidirect |
| 113. C8 | #10596941 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14557910 | 2 |
| #14557733 | 2 |
| #14557286 | 2 |
| #14557276 | 2 |
| C8×Q8×C37 | 2 |
| #1668 | 37 |