Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
154 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 59 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. #14557655 | C2 | semidirect |
| 2. #14557645 | C2 | semidirect |
| 3. #14557356 | C2 | semidirect |
| 4. #14557346 | C2 | semidirect |
| 5. #14557343 | C2 | semidirect |
| 6. #14557310 | C2 | semidirect |
| 18. SD32×C37 | C4 | semidirect |
| 19. D16×C37 | C4 | semidirect |
| 24. Q16×C37 | C2×C4 | semidirect |
| 28. D8×C37 | C2×C4 | semidirect |
| 37. C16×C37 | C2×C4 | semidirect |
| 76. C37 | AGL(1,ℤ/16) | semidirect |
| 81. SD32 | Dic37 | semidirect |
| 82. D16 | Dic37 | semidirect |
| 93. Q16 | C2×Dic37 | semidirect |
| 97. D8 | C2×Dic37 | semidirect |
| 107. C16 | C2×Dic37 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14557655 | 2 |
| #14557645 | 2 |
| #14557356 | 2 |
| #14557346 | 2 |
| #14557343 | 2 |
| #14557310 | 2 |
| C37×#509 | 2 |
| AGL(1,ℤ/16) | 37 |