Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
564 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 149 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×#11924566 | C2 | semidirect |
| 2. C2×#11924561 | C2 | semidirect |
| 3. C22×#10596930 | C2 | semidirect |
| 4. #14558104 | C2 | semidirect |
| 5. #14558097 | C2 | semidirect |
| 6. #14557926 | C2 | semidirect |
| 7. #14557921 | C2 | semidirect |
| 8. #14557914 | C2 | semidirect |
| 9. #14557904 | C2 | semidirect |
| 10. #14557488 | C2 | semidirect |
| 11. C2×#135×C37 | C2 | semidirect |
| 16. C2×#10596942 | C22 | semidirect |
| 20. C2×#10596940 | C22 | semidirect |
| 24. #11924534 | C22 | semidirect |
| 27. #11924523 | C22 | semidirect |
| 33. #11924446 | C22 | semidirect |
| 34. C8×Dic37 | C22 | semidirect |
| 38. C2×Q16×C37 | C22 | semidirect |
| 39. C2×SD16×C37 | C22 | semidirect |
| 40. C2×SD16×C37 | C22 | semidirect |
| 41. C2×D8×C37 | C22 | semidirect |
| 71. C2×C8×C37 | D4 | semidirect |
| 84. #10596934 | D4 | semidirect |
| 151. C2×#135 | D37 | semidirect |
| 160. C37 | #3154 | semidirect |
| 169. C2×Q16 | C2×D37 | semidirect |
| 175. C2×SD16 | C2×D37 | semidirect |
| 176. C2×SD16 | C2×D37 | semidirect |
| 178. C2×D8 | C2×D37 | semidirect |
| 228. C2×C8 | C22⋊D37 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11924566 | 2 |
| C2×#11924561 | 2 |
| C22×#10596930 | 2 |
| #14558104 | 2 |
| #14558097 | 2 |
| #14557926 | 2 |
| #14557921 | 2 |
| #14557914 | 2 |
| #14557904 | 2 |
| #14557488 | 2 |
| C2×#135×C37 | 2 |
| #3154 | 37 |