Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
540 conjugacy classes of subgroups; only the 177 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 177 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D37 |
| commutator | C22×C37 | C23×C4 |
| Fitting | C37×#383 | C2 |
| socle, cosocle | C23×C37 | C24 |
| prime radical | C22×D148 | C22 |
| hypercenter | #383 | D37 |
| hypocenter | C37 | #2337 |
| LCS | G ▷ C22×C37 ▷ C37 | |
| UCS | C1 ◁ C23 ◁ #383 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #14557437 | C2 | semidirect |
| 3. #14557425 | C2 | semidirect |
| 4. #14557422 | C2 | semidirect |
| 6. #14557407 | C2 | semidirect |
| 7. C4×C4⋊Dic37 | C2 | semidirect |
| 8. #14557380 | C2 | semidirect |
| 9. C37×#383 | C2 | semidirect |
| 13. #11924524 | C4 | semidirect |
| 47. C2×Dic74 | C2×C4 | semidirect |
| 48. C42×C37 | C2×C4 | semidirect |
| 52. #10596938 | C2×C4 | semidirect |
| 53. #10596938 | C2×C4 | semidirect |
| 125. #383 | 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 |
| #14557425 | 2 |
| #14557422 | 2 |
| #14557411 | 2 |
| #14557407 | 2 |
| C4×C4⋊Dic37 | 2 |
| #14557380 | 2 |
| C37×#383 | 2 |
| #2337 | 37 |