Finite Group DatabasebetaFinite Group DatabasebetaOrder 11072.
234 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 99 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×D173 |
| commutator, socle, cosocle | C22×C173 | C24 |
| Fitting | #123×C173 | C2 |
| prime radical | #19149651 | C2 |
| hypercenter | #123 | D173 |
| hypocenter | C173 | #529 |
| LCS | G ▷ C22×C173 ▷ C173 | |
| UCS | C1 ◁ C22 ◁ #123 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #19149674 | C2 | semidirect |
| 2. #19149672 | C2 | semidirect |
| 3. #19149669 | C2 | semidirect |
| 4. #19149665 | C2 | semidirect |
| 5. #19149662 | C2 | semidirect |
| 6. #19149656 | C2 | semidirect |
| 8. #19149644 | C2 | semidirect |
| 9. D4×Dic173 | C2 | semidirect |
| 10. #19149639 | C2 | semidirect |
| 11. #19149639 | C2 | semidirect |
| 12. #19149637 | C2 | semidirect |
| 13. #19149635 | C2 | semidirect |
| 14. C2×C4×Dic173 | C2 | semidirect |
| 15. #123×C173 | C2 | semidirect |
| 103. C173 | #529 | semidirect |
| 110. #123 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19149674 | 2 |
| #19149672 | 2 |
| #19149669 | 2 |
| #19149665 | 2 |
| #19149662 | 2 |
| #19149656 | 2 |
| #19149651 | 2 |
| #19149644 | 2 |
| D4×Dic173 | 2 |
| #19149639 | 2 |
| #19149637 | 2 |
| #19149635 | 2 |
| C2×C4×Dic173 | 2 |
| #123×C173 | 2 |
| #529 | 173 |