Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
392 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 139 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. Q8×Dic74 | C2 | semidirect |
| 3. #14557880 | C2 | semidirect |
| 4. #14557824 | C2 | semidirect |
| 5. #14557734 | C2 | semidirect |
| 6. C4×#10596930 | C2 | semidirect |
| 7. C8×Q8×C37 | C2 | semidirect |
| 44. Q8×C37 | SD16 | semidirect |
| 58. Dic74 | #41 | semidirect |
| 82. C8×Q8 | D37 | semidirect |
| 84. C37 | #3362 | semidirect |
| 124. Q8 | #10596930 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic74 | 2 |
| #14558205 | 2 |
| #14557880 | 2 |
| #14557824 | 2 |
| #14557734 | 2 |
| C4×#10596930 | 2 |
| C8×Q8×C37 | 2 |
| #3362 | 37 |