Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
388 conjugacy classes of subgroups; only the 195 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 195 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. #14557663 | C2 | semidirect |
| 3. #14557660 | C2 | semidirect |
| 4. Q8×#64436 | C2 | semidirect |
| 7. C8×Q8×C37 | C2 | semidirect |
| 42. #10596929 | Q8 | direct (N × H) |
| 44. Q8×C37 | M16 | semidirect |
| 57. C8×C37 | C2×Q8 | semidirect |
| 59. #64436 | C2×Q8 | semidirect |
| 80. C8×Q8 | D37 | semidirect |
| 83. C37 | Q8×M16 | semidirect |
| 121. Q8 | #10596929 | direct (N × H) |
| 135. C8 | Q8×D37 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×Q8×D37 | 2 |
| #14557663 | 2 |
| #14557660 | 2 |
| Q8×#64436 | 2 |
| #14557555 | 2 |
| C4×#10596929 | 2 |
| C8×Q8×C37 | 2 |
| Q8×M16 | 37 |