Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
420 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 420 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. D4×Dic74 | C2 | semidirect |
| 3. #14557884 | C2 | semidirect |
| 4. #14557864 | C2 | semidirect |
| 5. #14557819 | C2 | semidirect |
| 6. #14557762 | C2 | semidirect |
| 7. #14557739 | C2 | semidirect |
| 8. #14557674 | C2 | semidirect |
| 9. C4×#10596930 | C2 | semidirect |
| 10. C2×#11924461 | C2 | semidirect |
| 11. C8×D4×C37 | C2 | semidirect |
| 79. D4×C37 | SD16 | semidirect |
| 102. Dic74 | #41 | semidirect |
| 138. C8×D4 | D37 | semidirect |
| 140. C37 | #3298 | semidirect |
| 217. D4 | #10596930 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×Dic74 | 2 |
| #14558187 | 2 |
| #14557884 | 2 |
| #14557864 | 2 |
| #14557819 | 2 |
| #14557762 | 2 |
| #14557739 | 2 |
| #14557674 | 2 |
| C4×#10596930 | 2 |
| C2×#11924461 | 2 |
| C8×D4×C37 | 2 |
| #3298 | 37 |