Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
154 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 44 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. #14558579 | C2 | semidirect |
| 2. #14558574 | C2 | semidirect |
| 3. #14558458 | C2 | semidirect |
| 4. #14558451 | C2 | semidirect |
| 5. #14558450 | C2 | semidirect |
| 6. #14558423 | C2 | semidirect |
| 18. #11924479 | C4 | semidirect |
| 19. D592 | C4 | semidirect |
| 20. #11924477 | C4 | semidirect |
| 22. SD32×C37 | C4 | semidirect |
| 33. Q16×C37 | C2×C4 | semidirect |
| 38. D296 | C2×C4 | semidirect |
| 41. C16×C37 | C2×C4 | semidirect |
| 42. #10596925 | C2×C4 | semidirect |
| 83. C37 | AGL(1,ℤ/16) | semidirect |
| 89. SD32 | #3866 | semidirect |
| 102. Q16 | C2×#3866 | semidirect |
| 118. C16 | C2×#3866 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14558579 | 2 |
| #14558574 | 2 |
| #14558458 | 2 |
| #14558451 | 2 |
| #14558450 | 2 |
| #14558423 | 2 |
| #14557970 | 2 |
| AGL(1,ℤ/16) | 37 |