Finite Group DatabasebetaFinite Group DatabasebetaOrder 32192.
248 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 248 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. #30632857 | C2 | semidirect |
| 2. #30632857 | C2 | semidirect |
| 3. #30632850 | C2 | semidirect |
| 4. #30632848 | C2 | semidirect |
| 5. #30632847 | C2 | semidirect |
| 6. #30632846 | C2 | semidirect |
| 7. #30632843 | C2 | semidirect |
| 8. #30632841 | C2 | semidirect |
| 10. C4×C22⋊D503 | C2 | semidirect |
| 11. (C22⋊D503)⋊C4 | C2 | semidirect |
| 12. #30632823 | C2 | semidirect |
| 13. #30632820 | C2 | semidirect |
| 14. C2×C22⋊Dic503 | C2 | semidirect |
| 15. C2×C22⋊C4×C503 | C2 | semidirect |
| 16. C2×Dic1006 | C22 | semidirect |
| 22. C2×C4×D503 | C22 | semidirect |
| 23. C4⋊Dic503 | C22 | semidirect |
| 24. C4⋊Dic503 | C22 | semidirect |
| 25. C4⋊Dic503 | C22 | semidirect |
| 26. Dic503⋊C4 | C22 | semidirect |
| 27. Dic503⋊C4 | C22 | semidirect |
| 28. Dic503⋊C4 | C22 | semidirect |
| 29. Dic503⋊C4 | C22 | semidirect |
| 30. Dic503⋊C4 | C22 | semidirect |
| 38. (C2×D503)⋊C4 | C22 | semidirect |
| 39. (C2×D503)⋊C4 | C22 | semidirect |
| 40. (C2×D503)⋊C4 | C22 | semidirect |
| 41. C4×Dic503 | C22 | semidirect |
| 42. C4×Dic503 | C22 | semidirect |
| 43. C4×Dic503 | C22 | semidirect |
| 110. C503 | #551 | semidirect |
| 126. C2×C22⋊C4 | D503 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632857 | 2 |
| #30632850 | 2 |
| #30632848 | 2 |
| #30632847 | 2 |
| #30632846 | 2 |
| #30632843 | 2 |
| #30632841 | 2 |
| #30632833 | 2 |
| C4×C22⋊D503 | 2 |
| (C22⋊D503)⋊C4 | 2 |
| #30632823 | 2 |
| #30632820 | 2 |
| C2×C22⋊Dic503 | 2 |
| C2×C22⋊C4×C503 | 2 |
| #551 | 503 |