Finite Group DatabasebetaFinite Group DatabasebetaOrder 33344.
212 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 95 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×D521 |
| commutator, socle, cosocle | C22×C521 | C24 |
| Fitting | #126×C521 | C2 |
| prime radical | C2×C22⋊D521 | C22 |
| hypercenter | #126 | D521 |
| hypocenter | C521 | #556 |
| LCS | G ▷ C22×C521 ▷ C521 | |
| UCS | C1 ◁ C22 ◁ #126 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #30659707 | C2 | semidirect |
| 2. #30659703 | C2 | semidirect |
| 3. #30659703 | C2 | semidirect |
| 4. #30659701 | C2 | semidirect |
| 7. #30659686 | C2 | semidirect |
| 8. #30659685 | C2 | semidirect |
| 9. C4×Dic1042 | C2 | semidirect |
| 10. #30659673 | C2 | semidirect |
| 11. #30659673 | C2 | semidirect |
| 13. #30659665 | C2 | semidirect |
| 14. #30659664 | C2 | semidirect |
| 15. #126×C521 | C2 | semidirect |
| 97. C521 | #556 | semidirect |
| 103. #126 | D521 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30659707 | 2 |
| #30659703 | 2 |
| #30659701 | 2 |
| #30659694 | 2 |
| #30659686 | 2 |
| #30659685 | 2 |
| C4×Dic1042 | 2 |
| #30659673 | 2 |
| #30659668 | 2 |
| #30659665 | 2 |
| #30659664 | 2 |
| #126×C521 | 2 |
| #556 | 521 |