Finite Group DatabasebetaFinite Group DatabasebetaOrder 18752.
216 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 93 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 | #542 |
| 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. #22627623 | C2 | semidirect |
| 2. #22627619 | C2 | semidirect |
| 3. #22627612 | C2 | semidirect |
| 4. #22627610 | C2 | semidirect |
| 5. #22627610 | C2 | semidirect |
| 6. #22627609 | C2 | semidirect |
| 7. #22627608 | C2 | semidirect |
| 8. #22627604 | C2 | semidirect |
| 9. #22627602 | C2 | semidirect |
| 10. #22627601 | C2 | semidirect |
| 12. C4×Dic586 | C2 | semidirect |
| 13. #22627584 | C2 | semidirect |
| 14. #22627582 | C2 | semidirect |
| 15. #126×C293 | C2 | semidirect |
| 103. C293 | #542 | semidirect |
| 107. #126 | D293 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22627623 | 2 |
| #22627619 | 2 |
| #22627612 | 2 |
| #22627610 | 2 |
| #22627609 | 2 |
| #22627608 | 2 |
| #22627604 | 2 |
| #22627602 | 2 |
| #22627601 | 2 |
| #22627597 | 2 |
| C4×Dic586 | 2 |
| #22627584 | 2 |
| #22627582 | 2 |
| #126×C293 | 2 |
| #542 | 293 |