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 | #126×C283 | C2 |
| prime radical | #22583583 | C2 |
| hypercenter | #126 | D283 |
| hypocenter | C283 | #542 |
| LCS | G ▷ C22×C283 ▷ C283 | |
| UCS | C1 ◁ C22 ◁ #126 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #22583609 | C2 | semidirect |
| 2. #22583605 | C2 | semidirect |
| 3. #22583598 | C2 | semidirect |
| 4. #22583596 | C2 | semidirect |
| 5. #22583596 | C2 | semidirect |
| 6. #22583595 | C2 | semidirect |
| 7. #22583594 | C2 | semidirect |
| 8. #22583590 | C2 | semidirect |
| 9. #22583588 | C2 | semidirect |
| 10. #22583587 | C2 | semidirect |
| 12. C4×Dic566 | C2 | semidirect |
| 13. (C22⋊D283)⋊C4 | C2 | semidirect |
| 14. #22583568 | C2 | semidirect |
| 15. #126×C283 | C2 | semidirect |
| 103. C283 | #542 | semidirect |
| 107. #126 | 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 |
| #22583598 | 2 |
| #22583596 | 2 |
| #22583595 | 2 |
| #22583594 | 2 |
| #22583590 | 2 |
| #22583588 | 2 |
| #22583587 | 2 |
| #22583583 | 2 |
| C4×Dic566 | 2 |
| (C22⋊D283)⋊C4 | 2 |
| #22583568 | 2 |
| #126×C283 | 2 |
| #542 | 283 |