Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
572 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 145 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×#11924557 | C2 | semidirect |
| 2. #14558084 | C2 | semidirect |
| 3. #14558081 | C2 | semidirect |
| 4. #14557914 | C2 | semidirect |
| 5. #14557912 | C2 | semidirect |
| 6. #14557909 | C2 | semidirect |
| 7. #14557906 | C2 | semidirect |
| 8. C4×C8×D37 | C2 | semidirect |
| 9. C37×#492 | C2 | semidirect |
| 59. C8×D37 | D4 | semidirect |
| 91. C4×C37 | #135 | semidirect |
| 109. #492 | D37 | semidirect |
| 111. C37 | #3147 | semidirect |
| 196. C4 | #11924557 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11924557 | 2 |
| #14558084 | 2 |
| #14558081 | 2 |
| #14557914 | 2 |
| #14557912 | 2 |
| #14557909 | 2 |
| #14557906 | 2 |
| C4×C8×D37 | 2 |
| C37×#492 | 2 |
| #3147 | 37 |