Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
496 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 131 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. #14558081 | C2 | semidirect |
| 3. C4×#10596966 | C2 | semidirect |
| 4. #14557753 | C2 | semidirect |
| 5. #14557747 | C2 | semidirect |
| 6. #14557743 | C2 | semidirect |
| 7. #14557739 | C2 | semidirect |
| 8. #14557725 | C2 | semidirect |
| 9. C4⋊C8×D37 | C2 | semidirect |
| 10. #14557526 | C2 | semidirect |
| 11. C37×#460 | C2 | semidirect |
| 51. #10596966 | D4 | semidirect |
| 136. C4×C37 | #135 | semidirect |
| 158. #460 | D37 | semidirect |
| 162. C37 | #3035 | semidirect |
| 292. 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 |
| #14558081 | 2 |
| C4×#10596966 | 2 |
| #14557753 | 2 |
| #14557747 | 2 |
| #14557743 | 2 |
| #14557739 | 2 |
| #14557725 | 2 |
| C4⋊C8×D37 | 2 |
| #14557526 | 2 |
| C37×#460 | 2 |
| #3035 | 37 |