Finite Group DatabasebetaFinite Group DatabasebetaOrder 18112.
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×D283 |
| commutator, socle, cosocle | C22×C283 | C24 |
| Fitting | #123×C283 | C2 |
| prime radical | #22583582 | C2 |
| hypercenter | #123 | D283 |
| hypocenter | C283 | #542 |
| LCS | G ▷ C22×C283 ▷ C283 | |
| UCS | C1 ◁ C22 ◁ #123 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #22583609 | C2 | semidirect |
| 2. #22583605 | C2 | semidirect |
| 3. #22583603 | C2 | semidirect |
| 4. #22583597 | C2 | semidirect |
| 5. #22583596 | C2 | semidirect |
| 6. #22583596 | C2 | semidirect |
| 7. #22583592 | C2 | semidirect |
| 8. #22583589 | C2 | semidirect |
| 9. #22583588 | C2 | semidirect |
| 10. #22583587 | C2 | semidirect |
| 12. #22583575 | C2 | semidirect |
| 13. C4×C22⋊D283 | C2 | semidirect |
| 14. #22583566 | C2 | semidirect |
| 15. #123×C283 | C2 | semidirect |
| 103. C283 | #542 | semidirect |
| 112. #123 | D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22583609 | 2 |
| #22583605 | 2 |
| #22583603 | 2 |
| #22583597 | 2 |
| #22583596 | 2 |
| #22583592 | 2 |
| #22583589 | 2 |
| #22583588 | 2 |
| #22583587 | 2 |
| #22583582 | 2 |
| #22583575 | 2 |
| C4×C22⋊D283 | 2 |
| #22583566 | 2 |
| #123×C283 | 2 |
| #542 | 283 |