Finite Group DatabasebetaFinite Group DatabasebetaOrder 19904.
268 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 268 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. #23755753 | C2 | semidirect |
| 2. #23755734 | C2 | semidirect |
| 3. #23755732 | C2 | semidirect |
| 4. #23755730 | C2 | semidirect |
| 5. #23755727 | C2 | semidirect |
| 6. D8×D311 | C2 | semidirect |
| 7. #23755714 | C2 | semidirect |
| 8. C2×D8×C311 | C2 | semidirect |
| 10. #19097315 | C22 | semidirect |
| 12. #19097314 | C22 | semidirect |
| 15. D4×D311 | C22 | semidirect |
| 16. Dic1244 | C22 | semidirect |
| 17. #19097304 | C22 | semidirect |
| 18. #19097303 | C22 | semidirect |
| 19. D2488 | C22 | semidirect |
| 20. #19097300 | C22 | semidirect |
| 21. #19097299 | C22 | semidirect |
| 22. #19097298 | C22 | semidirect |
| 23. C8×D311 | C22 | semidirect |
| 24. C2×D4×C311 | C22 | semidirect |
| 25. D8×C311 | C22 | semidirect |
| 26. D8×C311 | C22 | semidirect |
| 27. C2×C8×C311 | C22 | semidirect |
| 62. C311 | #576 | semidirect |
| 70. C2×D8 | D311 | semidirect |
| 79. C2×D4 | C2×D311 | semidirect |
| 85. D8 | C2×D311 | semidirect |
| 86. D8 | C2×D311 | semidirect |
| 90. C2×C8 | C2×D311 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23755753 | 2 |
| #23755734 | 2 |
| #23755732 | 2 |
| #23755730 | 2 |
| #23755727 | 2 |
| D8×D311 | 2 |
| #23755714 | 2 |
| C2×D8×C311 | 2 |
| #576 | 311 |