Finite Group DatabasebetaFinite Group DatabasebetaOrder 17728.
250 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 250 conjugacy classes of subgroups — too many to draw. Only its 95 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×D277 |
| commutator, socle, cosocle | C22×C277 | C24 |
| Fitting | #120×C277 | C2 |
| hypercenter | #120 | D277 |
| hypocenter | C277 | #538 |
| LCS | G ▷ C22×C277 ▷ C277 | |
| UCS | C1 ◁ C22 ◁ #120 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #22579873 | C2 | semidirect |
| 2. #22579873 | C2 | semidirect |
| 3. #22579867 | C2 | semidirect |
| 4. #22579866 | C2 | semidirect |
| 5. #22579862 | C2 | semidirect |
| 6. #22579861 | C2 | semidirect |
| 7. #22579857 | C2 | semidirect |
| 8. #22579852 | C2 | semidirect |
| 9. #22579852 | C2 | semidirect |
| 10. #22579851 | C2 | semidirect |
| 11. #22579849 | C2 | semidirect |
| 12. D4×Dic277 | C2 | semidirect |
| 13. #22579840 | C2 | semidirect |
| 14. C2×C22⋊Dic277 | C2 | semidirect |
| 15. #120×C277 | C2 | semidirect |
| 16. C2×Dic554 | C22 | semidirect |
| 20. C2×C22⋊D277 | C22 | semidirect |
| 23. C22×Dic277 | C22 | semidirect |
| 24. C2×C4×D277 | C22 | semidirect |
| 25. C4⋊Dic277 | C22 | semidirect |
| 26. C4⋊Dic277 | C22 | semidirect |
| 27. #17984542 | C22 | semidirect |
| 28. #17984542 | C22 | semidirect |
| 29. #17984542 | C22 | semidirect |
| 30. #17984542 | C22 | semidirect |
| 38. C22⋊Dic277 | C22 | semidirect |
| 39. C22⋊Dic277 | C22 | semidirect |
| 40. #17984540 | C22 | semidirect |
| 41. #17984540 | C22 | semidirect |
| 42. C4×Dic277 | C22 | semidirect |
| 43. C4×Dic277 | C22 | semidirect |
| 116. C277 | #538 | semidirect |
| 129. #120 | D277 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22579873 | 2 |
| #22579867 | 2 |
| #22579866 | 2 |
| #22579862 | 2 |
| #22579861 | 2 |
| #22579857 | 2 |
| #22579852 | 2 |
| #22579851 | 2 |
| #22579849 | 2 |
| D4×Dic277 | 2 |
| #22579840 | 2 |
| C2×C22⋊Dic277 | 2 |
| #120×C277 | 2 |
| #538 | 277 |