Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
732 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 732 conjugacy classes of subgroups — too many to draw. Only its 165 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. C2×#11924561 | C2 | semidirect |
| 2. C22×#10596941 | C2 | semidirect |
| 3. #14558097 | C2 | semidirect |
| 4. #14557678 | C2 | semidirect |
| 5. #14557672 | C2 | semidirect |
| 6. #14557542 | C2 | semidirect |
| 7. #14557529 | C2 | semidirect |
| 8. #14557500 | C2 | semidirect |
| 9. C2×2−1+4×C37 | C2 | semidirect |
| 23. #11924460 | C22 | semidirect |
| 24. #11924460 | C22 | semidirect |
| 25. #11924457 | C22 | semidirect |
| 26. C22⋊#64436 | C22 | semidirect |
| 33. C2×#41×C37 | C22 | semidirect |
| 36. C22×Q8×C37 | C22 | semidirect |
| 45. #41×C37 | D4 | semidirect |
| 53. C2×Q8×C37 | D4 | semidirect |
| 146. C2×2−1+4 | D37 | semidirect |
| 155. C37 | #3010 | semidirect |
| 162. C2×#41 | C2×D37 | semidirect |
| 165. C22×Q8 | C2×D37 | semidirect |
| 191. #41 | C22⋊D37 | semidirect |
| 199. C2×Q8 | C22⋊D37 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11924561 | 2 |
| C22×#10596941 | 2 |
| #14558097 | 2 |
| #14557678 | 2 |
| #14557672 | 2 |
| #14557542 | 2 |
| #14557529 | 2 |
| #14557500 | 2 |
| C2×2−1+4×C37 | 2 |
| #3010 | 37 |