Finite Group DatabasebetaFinite Group DatabasebetaOrder 18752.
234 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 97 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×D293 |
| commutator, socle, cosocle | C22×C293 | C24 |
| Fitting | #126×C293 | C2 |
| prime radical | #22627597 | C2 |
| hypercenter | #126 | D293 |
| hypocenter | C293 | #529 |
| LCS | G ▷ C22×C293 ▷ C293 | |
| UCS | C1 ◁ C22 ◁ #126 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #22627618 | C2 | semidirect |
| 2. #22627614 | C2 | semidirect |
| 3. #22627610 | C2 | semidirect |
| 4. #22627609 | C2 | semidirect |
| 5. #22627606 | C2 | semidirect |
| 6. #22627602 | C2 | semidirect |
| 8. #22627589 | C2 | semidirect |
| 9. #22627586 | C2 | semidirect |
| 10. #22627584 | C2 | semidirect |
| 11. #22627584 | C2 | semidirect |
| 12. #22627582 | C2 | semidirect |
| 13. #22627580 | C2 | semidirect |
| 14. C42×D293 | C2 | semidirect |
| 15. #126×C293 | C2 | semidirect |
| 103. C293 | #529 | semidirect |
| 106. #126 | D293 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22627618 | 2 |
| #22627614 | 2 |
| #22627610 | 2 |
| #22627609 | 2 |
| #22627606 | 2 |
| #22627602 | 2 |
| #22627597 | 2 |
| #22627589 | 2 |
| #22627586 | 2 |
| #22627584 | 2 |
| #22627582 | 2 |
| #22627580 | 2 |
| C42×D293 | 2 |
| #126×C293 | 2 |
| #529 | 293 |