Finite Group DatabasebetaFinite Group DatabasebetaOrder 17728.
428 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 115 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 | #121×C277 | C2 |
| hypercenter | #121 | D277 |
| hypocenter | C277 | D42 |
| LCS | G ▷ C22×C277 ▷ C277 | |
| UCS | C1 ◁ C22 ◁ #121 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×D1108 | C2 | semidirect |
| 2. C2×D4×D277 | C2 | semidirect |
| 3. C2×D4×D277 | C2 | semidirect |
| 4. #22579876 | C2 | semidirect |
| 5. #22579855 | C2 | semidirect |
| 6. #22579853 | C2 | semidirect |
| 7. #22579850 | C2 | semidirect |
| 8. #22579848 | C2 | semidirect |
| 9. #22579842 | C2 | semidirect |
| 10. C4×C22⋊D277 | C2 | semidirect |
| 11. #121×C277 | C2 | semidirect |
| 12. C23×D277 | C22 | semidirect |
| 13. C23×D277 | C22 | semidirect |
| 16. C2×D1108 | C22 | semidirect |
| 17. C2×D1108 | C22 | semidirect |
| 18. C2×D1108 | C22 | semidirect |
| 20. C2×C22⋊D277 | C22 | semidirect |
| 21. C2×C22⋊D277 | C22 | semidirect |
| 22. C2×C22⋊D277 | C22 | semidirect |
| 25. C2×C4×D277 | C22 | semidirect |
| 26. C2×C4×D277 | C22 | semidirect |
| 27. #17984542 | C22 | semidirect |
| 28. C22⋊Dic277 | C22 | semidirect |
| 29. #17984540 | C22 | semidirect |
| 30. #17984540 | C22 | semidirect |
| 31. #17984540 | C22 | semidirect |
| 32. C4×Dic277 | C22 | semidirect |
| 33. C2×D4×C277 | C22 | semidirect |
| 34. C2×D4×C277 | C22 | semidirect |
| 35. C22×C4×C277 | C22 | semidirect |
| 36. C4⋊C4×C277 | C22 | semidirect |
| 37. C22⋊C4×C277 | C22 | semidirect |
| 50. D1108 | D4 | semidirect |
| 54. C22⋊D277 | D4 | semidirect |
| 73. C22×C277 | C2×D4 | semidirect |
| 84. C2×D277 | C2×D4 | semidirect |
| 85. C2×D277 | C2×D4 | semidirect |
| 88. C4×C277 | C2×D4 | semidirect |
| 91. Dic277 | C2×D4 | semidirect |
| 100. C277 | D42 | semidirect |
| 108. #121 | D277 | semidirect |
| 126. C2×D4 | C2×D277 | semidirect |
| 127. C2×D4 | C2×D277 | semidirect |
| 130. C22×C4 | C2×D277 | semidirect |
| 132. C4⋊C4 | C2×D277 | semidirect |
| 137. C22⋊C4 | C2×D277 | semidirect |
| 185. C22 | D4×D277 | semidirect |
| 192. C4 | D4×D277 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D1108 | 2 |
| C2×D4×D277 | 2 |
| #22579876 | 2 |
| #22579855 | 2 |
| #22579853 | 2 |
| #22579850 | 2 |
| #22579848 | 2 |
| #22579842 | 2 |
| C4×C22⋊D277 | 2 |
| #121×C277 | 2 |
| D42 | 277 |