Finite Group DatabasebetaFinite Group DatabasebetaOrder 21568.
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. #24925004 | C2 | semidirect |
| 2. #24924985 | C2 | semidirect |
| 3. #24924983 | C2 | semidirect |
| 4. #24924981 | C2 | semidirect |
| 5. #24924978 | C2 | semidirect |
| 6. D8×D337 | C2 | semidirect |
| 7. #24924965 | C2 | semidirect |
| 8. C2×D8×C337 | C2 | semidirect |
| 10. #19129185 | C22 | semidirect |
| 12. #19129184 | C22 | semidirect |
| 15. D4×D337 | C22 | semidirect |
| 16. Dic1348 | C22 | semidirect |
| 17. #19129174 | C22 | semidirect |
| 18. #19129173 | C22 | semidirect |
| 19. D2696 | C22 | semidirect |
| 20. #19129170 | C22 | semidirect |
| 21. #19129169 | C22 | semidirect |
| 22. #19129168 | C22 | semidirect |
| 23. C8×D337 | C22 | semidirect |
| 24. C2×D4×C337 | C22 | semidirect |
| 25. D8×C337 | C22 | semidirect |
| 26. D8×C337 | C22 | semidirect |
| 27. C2×C8×C337 | C22 | semidirect |
| 62. C337 | #576 | semidirect |
| 70. C2×D8 | D337 | semidirect |
| 79. C2×D4 | C2×D337 | semidirect |
| 85. D8 | C2×D337 | semidirect |
| 86. D8 | C2×D337 | semidirect |
| 90. C2×C8 | C2×D337 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24925004 | 2 |
| #24924985 | 2 |
| #24924983 | 2 |
| #24924981 | 2 |
| #24924978 | 2 |
| D8×D337 | 2 |
| #24924965 | 2 |
| C2×D8×C337 | 2 |
| #576 | 337 |