Finite Group DatabasebetaFinite Group DatabasebetaOrder 18112.
334 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 334 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 | #127×C283 | C2 |
| hypercenter | #127 | D283 |
| hypocenter | C283 | #535 |
| LCS | G ▷ C22×C283 ▷ C283 | |
| UCS | C1 ◁ C22 ◁ #127 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#17985391 | C2 | semidirect |
| 2. C2×D4×D283 | C2 | semidirect |
| 3. #22583606 | C2 | semidirect |
| 4. #22583598 | C2 | semidirect |
| 5. #22583597 | C2 | semidirect |
| 6. #22583582 | C2 | semidirect |
| 7. #22583578 | C2 | semidirect |
| 8. #22583567 | C2 | semidirect |
| 9. #127×C283 | C2 | semidirect |
| 12. C2×Dic566 | C22 | semidirect |
| 16. C2×C22⋊D283 | C22 | semidirect |
| 18. C22×Dic283 | C22 | semidirect |
| 20. Dic283⋊C4 | C22 | semidirect |
| 21. C22⋊Dic283 | C22 | semidirect |
| 23. (C2×D283)⋊C4 | C22 | semidirect |
| 24. C4×Dic283 | C22 | semidirect |
| 26. C2×D4×C283 | C22 | semidirect |
| 27. C2×D4×C283 | C22 | semidirect |
| 28. C42×C283 | C22 | semidirect |
| 42. C4×D283 | D4 | semidirect |
| 71. C283 | #535 | semidirect |
| 76. #127 | D283 | semidirect |
| 91. C2×D4 | C2×D283 | semidirect |
| 92. C2×D4 | C2×D283 | semidirect |
| 100. C42 | C2×D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17985391 | 2 |
| C2×D4×D283 | 2 |
| #22583606 | 2 |
| #22583598 | 2 |
| #22583597 | 2 |
| #22583582 | 2 |
| #22583578 | 2 |
| #22583567 | 2 |
| #127×C283 | 2 |
| #535 | 283 |