Finite Group DatabasebetaFinite Group DatabasebetaOrder 20032.
270 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 103 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D313 |
| commutator, socle, cosocle | C22×C313 | C24 |
| Fitting | #123×C313 | C2 |
| prime radical | C2×#19097560 | C2 |
| hypercenter | #123 | D313 |
| hypocenter | C313 | #536 |
| LCS | G ▷ C22×C313 ▷ C313 | |
| UCS | C1 ◁ C22 ◁ #123 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C22×Dic626 | C2 | semidirect |
| 3. #23756496 | C2 | semidirect |
| 4. #23756483 | C2 | semidirect |
| 5. #23756481 | C2 | semidirect |
| 6. #23756480 | C2 | semidirect |
| 7. #23756478 | C2 | semidirect |
| 8. #23756475 | C2 | semidirect |
| 9. #23756474 | C2 | semidirect |
| 10. #23756453 | C2 | semidirect |
| 11. #123×C313 | C2 | semidirect |
| 79. C313 | #536 | semidirect |
| 88. #123 | D313 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097560 | 2 |
| C22×Dic626 | 2 |
| #23756496 | 2 |
| #23756483 | 2 |
| #23756481 | 2 |
| #23756480 | 2 |
| #23756478 | 2 |
| #23756475 | 2 |
| #23756474 | 2 |
| #23756453 | 2 |
| #123×C313 | 2 |
| #536 | 313 |