Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
386 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 121 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. #14558138 | C2 | semidirect |
| 2. #14557932 | C2 | semidirect |
| 3. #14557909 | C2 | semidirect |
| 4. #14557899 | C2 | semidirect |
| 5. #14557897 | C2 | semidirect |
| 6. #14557784 | C2 | semidirect |
| 7. #14557767 | C2 | semidirect |
| 8. #14557643 | C2 | semidirect |
| 9. C4×#10596939 | C2 | semidirect |
| 10. #14557489 | C2 | semidirect |
| 11. C37×#540 | C2 | semidirect |
| 116. #540 | D37 | semidirect |
| 126. C37 | #3176 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14558138 | 2 |
| #14557932 | 2 |
| #14557909 | 2 |
| #14557899 | 2 |
| #14557897 | 2 |
| #14557784 | 2 |
| #14557767 | 2 |
| #14557643 | 2 |
| C4×#10596939 | 2 |
| #14557489 | 2 |
| C37×#540 | 2 |
| #3176 | 37 |