Finite Group DatabasebetaFinite Group DatabasebetaOrder 19904.
262 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 1. #41×D311 | C2 | semidirect |
| 2. #23755740 | C2 | semidirect |
| 3. #23755737 | C2 | semidirect |
| 4. #23755735 | C2 | semidirect |
| 5. #23755732 | C2 | semidirect |
| 6. #23755730 | C2 | semidirect |
| 7. #23755728 | C2 | semidirect |
| 8. C2×#19097298 | C2 | semidirect |
| 9. #135×C311 | C2 | semidirect |
| 12. #19097315 | C22 | semidirect |
| 15. Q8×D311 | C22 | semidirect |
| 17. D4×D311 | C22 | semidirect |
| 20. Dic1244 | C22 | semidirect |
| 21. #19097305 | C22 | semidirect |
| 22. #19097304 | C22 | semidirect |
| 23. #19097303 | C22 | semidirect |
| 24. #19097302 | C22 | semidirect |
| 25. D2488 | C22 | semidirect |
| 26. #19097300 | C22 | semidirect |
| 27. #19097298 | C22 | semidirect |
| 28. #19097298 | C22 | semidirect |
| 29. C2×C311⋊C8 | C22 | semidirect |
| 30. #41×C311 | C22 | semidirect |
| 31. Q16×C311 | C22 | semidirect |
| 32. SD16×C311 | C22 | semidirect |
| 33. D8×C311 | C22 | semidirect |
| 34. C2×C8×C311 | C22 | semidirect |
| 75. C311 | #575 | semidirect |
| 84. #135 | D311 | semidirect |
| 91. #41 | C2×D311 | semidirect |
| 99. Q16 | C2×D311 | semidirect |
| 103. SD16 | C2×D311 | semidirect |
| 106. D8 | C2×D311 | semidirect |
| 110. C2×C8 | C2×D311 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #41×D311 | 2 |
| #23755740 | 2 |
| #23755737 | 2 |
| #23755735 | 2 |
| #23755732 | 2 |
| #23755730 | 2 |
| #23755728 | 2 |
| C2×#19097298 | 2 |
| #135×C311 | 2 |
| #575 | 311 |