Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
792 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 792 conjugacy classes of subgroups — too many to draw. Only its 269 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 |
|---|---|---|
| 2. C23×#64436 | C2 | semidirect |
| 3. #14557527 | C2 | direct (N × H) |
| 4. C2×#11924459 | C2 | semidirect |
| 5. C2×#11924456 | C2 | semidirect |
| 6. C2×#117×C37 | C2 | semidirect |
| 9. C2×#10596962 | C4 | semidirect |
| 17. C22×#64436 | C22 | semidirect |
| 18. #11924459 | C22 | semidirect |
| 19. #11924456 | C22 | semidirect |
| 22. #117×C37 | C22 | semidirect |
| 40. #10596962 | C2×C4 | semidirect |
| 104. C2×C37 | #416 | semidirect |
| 110. C2×#117 | D37 | semidirect |
| 114. C37 | C2×#416 | semidirect |
| 128. #117 | C2×D37 | semidirect |
| 212. C2 | #14557527 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#10596962 | 2 |
| C23×#64436 | 2 |
| #14557527 | 2 |
| C2×#11924459 | 2 |
| C2×#11924456 | 2 |
| C2×#117×C37 | 2 |
| C2×#416 | 37 |