Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
656 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 157 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×#11924562 | C2 | semidirect |
| 2. #14558083 | C2 | semidirect |
| 3. #14557920 | C2 | semidirect |
| 4. #14557909 | C2 | semidirect |
| 5. #14557905 | C2 | semidirect |
| 6. C4×#10596934 | C2 | semidirect |
| 7. C2×#127×C37 | C2 | semidirect |
| 10. C2×#10596940 | C22 | semidirect |
| 11. C2×#10596939 | C22 | semidirect |
| 13. #11924536 | C22 | semidirect |
| 14. #11924533 | C22 | semidirect |
| 15. #11924524 | C22 | semidirect |
| 18. #11924447 | C22 | semidirect |
| 19. C4×#64436 | C22 | semidirect |
| 48. #10596934 | D4 | semidirect |
| 71. #64436 | C2×D4 | semidirect |
| 82. C4×C37 | AGL(1,ℤ/8) | semidirect |
| 93. C2×#127 | D37 | semidirect |
| 98. C37 | #3151 | semidirect |
| 174. C4 | #11924562 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11924562 | 2 |
| #14558083 | 2 |
| #14557920 | 2 |
| #14557909 | 2 |
| #14557905 | 2 |
| C4×#10596934 | 2 |
| C2×#127×C37 | 2 |
| #3151 | 37 |