Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
540 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 181 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. #14557437 | C2 | semidirect |
| 3. #14557424 | C2 | semidirect |
| 4. #14557423 | C2 | semidirect |
| 6. #14557404 | C2 | semidirect |
| 7. #14557401 | C2 | semidirect |
| 8. C4×#10596938 | C2 | semidirect |
| 9. C4×C4⋊C4×C37 | C2 | semidirect |
| 13. #11924524 | C4 | semidirect |
| 47. C2×Dic74 | C2×C4 | semidirect |
| 51. C42×C37 | C2×C4 | semidirect |
| 55. #10596938 | C2×C4 | semidirect |
| 56. #10596938 | C2×C4 | semidirect |
| 126. C4×C4⋊C4 | D37 | semidirect |
| 128. C37 | #2337 | semidirect |
| 177. C42 | C4×D37 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11924524 | 2 |
| #14557437 | 2 |
| #14557424 | 2 |
| #14557423 | 2 |
| #14557411 | 2 |
| #14557404 | 2 |
| #14557401 | 2 |
| C4×#10596938 | 2 |
| C4×C4⋊C4×C37 | 2 |
| #2337 | 37 |