Finite Group DatabasebetaFinite Group DatabasebetaOrder 20032.
330 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
| hypercenter | #123 | D313 |
| hypocenter | C313 | #525 |
| LCS | G ▷ C22×C313 ▷ C313 | |
| UCS | C1 ◁ C22 ◁ #123 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#19097560 | C2 | semidirect |
| 2. C22×C4×D313 | C2 | semidirect |
| 3. #23756480 | C2 | semidirect |
| 4. #23756475 | C2 | semidirect |
| 5. #23756470 | C2 | semidirect |
| 6. #23756467 | C2 | semidirect |
| 7. #23756465 | C2 | semidirect |
| 8. #23756459 | C2 | semidirect |
| 9. #23756457 | C2 | semidirect |
| 10. #23756453 | C2 | semidirect |
| 11. #123×C313 | C2 | semidirect |
| 14. C2×Dic626 | C22 | semidirect |
| 18. C2×C22⋊D313 | C22 | semidirect |
| 20. C22×Dic313 | C22 | semidirect |
| 24. C2×C4×D313 | C22 | semidirect |
| 25. #19097540 | C22 | semidirect |
| 26. #19097540 | C22 | semidirect |
| 30. #19097538 | C22 | semidirect |
| 31. C4×Dic313 | C22 | semidirect |
| 34. C4⋊C4×C313 | C22 | semidirect |
| 36. C22⋊C4×C313 | C22 | semidirect |
| 47. C2×Dic313 | D4 | semidirect |
| 72. C2×D313 | #41 | semidirect |
| 86. C313 | #525 | semidirect |
| 91. #123 | D313 | semidirect |
| 116. C4⋊C4 | C2×D313 | semidirect |
| 122. C22⋊C4 | C2×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×C4×D313 | 2 |
| #23756480 | 2 |
| #23756475 | 2 |
| #23756470 | 2 |
| #23756467 | 2 |
| #23756465 | 2 |
| #23756459 | 2 |
| #23756457 | 2 |
| #23756453 | 2 |
| #123×C313 | 2 |
| #525 | 313 |