Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
396 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 123 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. #14558243 | C2 | semidirect |
| 2. #14557897 | C2 | semidirect |
| 3. #14557879 | C2 | semidirect |
| 4. #14557833 | C2 | semidirect |
| 5. #14557823 | C2 | semidirect |
| 6. #14557725 | C2 | semidirect |
| 7. #14557725 | C2 | semidirect |
| 8. #14557664 | C2 | semidirect |
| 9. #14557643 | C2 | semidirect |
| 10. C4×#10596939 | C2 | semidirect |
| 11. C37×#550 | C2 | semidirect |
| 97. D148 | #41 | semidirect |
| 131. #550 | D37 | semidirect |
| 141. C37 | #3366 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14558243 | 2 |
| #14557897 | 2 |
| #14557879 | 2 |
| #14557833 | 2 |
| #14557823 | 2 |
| #14557725 | 2 |
| #14557664 | 2 |
| #14557643 | 2 |
| C4×#10596939 | 2 |
| C37×#550 | 2 |
| #3366 | 37 |