Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
494 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 141 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. C22×#10596940 | C2 | semidirect |
| 2. #14558104 | C2 | semidirect |
| 3. #14558008 | C2 | semidirect |
| 4. #14557746 | C2 | semidirect |
| 5. #14557736 | C2 | semidirect |
| 6. #14557561 | C2 | semidirect |
| 7. #14557543 | C2 | semidirect |
| 8. #14557529 | C2 | semidirect |
| 14. #11924534 | C22 | semidirect |
| 15. #11924523 | C22 | semidirect |
| 23. #11924465 | C22 | semidirect |
| 24. #11924461 | C22 | semidirect |
| 25. #11924460 | C22 | semidirect |
| 26. #11924457 | C22 | semidirect |
| 126. C37 | #3042 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#10596940 | 2 |
| #14558104 | 2 |
| #14558008 | 2 |
| #14557746 | 2 |
| #14557736 | 2 |
| #14557561 | 2 |
| #14557543 | 2 |
| #14557529 | 2 |
| C2×AGL(1,ℤ/8)×C37 | 2 |
| #3042 | 37 |