Finite Group DatabasebetaFinite Group DatabasebetaOrder 26176.
258 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 101 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×Q8×D409 | C2 | semidirect |
| 3. #27189750 | C2 | semidirect |
| 4. #27189749 | C2 | semidirect |
| 5. #27189748 | C2 | semidirect |
| 6. #27189747 | C2 | semidirect |
| 7. #27189746 | C2 | semidirect |
| 8. Q16×D409 | C2 | semidirect |
| 9. SD16×D409 | C2 | semidirect |
| 10. M16×D409 | C2 | semidirect |
| 11. #137×C409 | C2 | semidirect |
| 18. C2×Dic818 | C22 | semidirect |
| 23. Q8×D409 | C22 | semidirect |
| 29. Dic1636 | C22 | semidirect |
| 30. #20266978 | C22 | semidirect |
| 31. #20266978 | C22 | semidirect |
| 32. #20266977 | C22 | semidirect |
| 33. #20266976 | C22 | semidirect |
| 34. #20266975 | C22 | semidirect |
| 35. #20266972 | C22 | semidirect |
| 36. #20266971 | C22 | semidirect |
| 39. C2×Q8×C409 | C22 | semidirect |
| 40. Q16×C409 | C22 | semidirect |
| 41. SD16×C409 | C22 | semidirect |
| 42. M16×C409 | C22 | semidirect |
| 98. D409 | #137 | direct (N × H) |
| 99. C409 | C2×#137 | semidirect |
| 108. #137 | D409 | direct (N × H) |
| 125. C2×Q8 | C2×D409 | semidirect |
| 134. Q16 | C2×D409 | semidirect |
| 138. SD16 | C2×D409 | semidirect |
| 141. M16 | C2×D409 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #41×D409 | 2 |
| C2×Q8×D409 | 2 |
| #27189750 | 2 |
| #27189749 | 2 |
| #27189748 | 2 |
| #27189747 | 2 |
| #27189746 | 2 |
| Q16×D409 | 2 |
| SD16×D409 | 2 |
| M16×D409 | 2 |
| #137×C409 | 2 |
| C2×#137 | 409 |