Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
494 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 125 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×#11924555 | C2 | semidirect |
| 2. #14558203 | C2 | semidirect |
| 3. #14558187 | C2 | semidirect |
| 4. #14557905 | C2 | semidirect |
| 5. #14557761 | C2 | semidirect |
| 6. #14557744 | C2 | semidirect |
| 7. #14557696 | C2 | semidirect |
| 8. #14557675 | C2 | semidirect |
| 9. C4×#10596940 | C2 | semidirect |
| 10. #14557598 | C2 | semidirect |
| 11. C37×#459 | C2 | semidirect |
| 68. #10596940 | D4 | semidirect |
| 127. C4×C37 | #135 | semidirect |
| 147. #459 | D37 | semidirect |
| 152. C37 | #3284 | semidirect |
| 272. C4 | #11924555 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11924555 | 2 |
| #14558203 | 2 |
| #14558187 | 2 |
| #14557905 | 2 |
| #14557761 | 2 |
| #14557744 | 2 |
| #14557696 | 2 |
| #14557675 | 2 |
| C4×#10596940 | 2 |
| #14557598 | 2 |
| C37×#459 | 2 |
| #3284 | 37 |