Finite Group DatabasebetaFinite Group DatabasebetaOrder 25664.
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×D401 | C2 | semidirect |
| 3. #27165770 | C2 | semidirect |
| 4. #27165769 | C2 | semidirect |
| 5. #27165768 | C2 | semidirect |
| 6. #27165767 | C2 | semidirect |
| 7. #27165766 | C2 | semidirect |
| 8. Q16×D401 | C2 | semidirect |
| 9. SD16×D401 | C2 | semidirect |
| 10. M16×D401 | C2 | semidirect |
| 11. #137×C401 | C2 | semidirect |
| 18. C2×Dic802 | C22 | semidirect |
| 23. Q8×D401 | C22 | semidirect |
| 29. Dic1604 | C22 | semidirect |
| 30. #20264356 | C22 | semidirect |
| 31. #20264356 | C22 | semidirect |
| 32. #20264355 | C22 | semidirect |
| 33. #20264354 | C22 | semidirect |
| 34. #20264353 | C22 | semidirect |
| 35. #20264350 | C22 | semidirect |
| 36. #20264349 | C22 | semidirect |
| 39. C2×Q8×C401 | C22 | semidirect |
| 40. Q16×C401 | C22 | semidirect |
| 41. SD16×C401 | C22 | semidirect |
| 42. M16×C401 | C22 | semidirect |
| 98. D401 | #137 | direct (N × H) |
| 99. C401 | C2×#137 | semidirect |
| 108. #137 | D401 | direct (N × H) |
| 125. C2×Q8 | C2×D401 | semidirect |
| 134. Q16 | C2×D401 | semidirect |
| 138. SD16 | C2×D401 | semidirect |
| 141. M16 | C2×D401 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #41×D401 | 2 |
| C2×Q8×D401 | 2 |
| #27165770 | 2 |
| #27165769 | 2 |
| #27165768 | 2 |
| #27165767 | 2 |
| #27165766 | 2 |
| Q16×D401 | 2 |
| SD16×D401 | 2 |
| M16×D401 | 2 |
| #137×C401 | 2 |
| C2×#137 | 401 |