Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
568 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 205 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×#382 | C2 |
| socle, cosocle | C23×C37 | C24 |
| prime radical | C23×D37 | C23 |
| hypercenter | #382 | D37 |
| hypocenter | C37 | #2283 |
| LCS | G ▷ C22×C37 ▷ C37 | |
| UCS | C1 ◁ C23 ◁ #382 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #14557400 | C2 | semidirect |
| 3. #14557399 | C2 | semidirect |
| 6. C4⋊C4×Dic37 | C2 | semidirect |
| 8. #14557378 | C2 | semidirect |
| 9. C37×#382 | C2 | semidirect |
| 19. C42×D37 | C4 | semidirect |
| 109. #382 | D37 | semidirect |
| 115. C37 | #2283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C42×D37 | 2 |
| #14557400 | 2 |
| #14557399 | 2 |
| #14557395 | 2 |
| #14557390 | 2 |
| C4⋊C4×Dic37 | 2 |
| #14557380 | 2 |
| #14557378 | 2 |
| C37×#382 | 2 |
| #2283 | 37 |