Finite Group DatabasebetaFinite Group DatabasebetaOrder 18112.
270 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 103 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 | C2×#17985391 | C2 |
| hypercenter | #123 | D283 |
| hypocenter | C283 | #536 |
| LCS | G ▷ C22×C283 ▷ C283 | |
| UCS | C1 ◁ C22 ◁ #123 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C22×Dic566 | C2 | semidirect |
| 3. #22583609 | C2 | semidirect |
| 4. #22583596 | C2 | semidirect |
| 5. #22583594 | C2 | semidirect |
| 6. #22583593 | C2 | semidirect |
| 7. #22583591 | C2 | semidirect |
| 8. #22583588 | C2 | semidirect |
| 9. #22583587 | C2 | semidirect |
| 10. #22583566 | C2 | semidirect |
| 11. #123×C283 | C2 | semidirect |
| 79. C283 | #536 | semidirect |
| 88. #123 | D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17985391 | 2 |
| C22×Dic566 | 2 |
| #22583609 | 2 |
| #22583596 | 2 |
| #22583594 | 2 |
| #22583593 | 2 |
| #22583591 | 2 |
| #22583588 | 2 |
| #22583587 | 2 |
| #22583566 | 2 |
| #123×C283 | 2 |
| #536 | 283 |