Finite Group DatabasebetaFinite Group DatabasebetaOrder 29888.
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. #28417946 | C2 | semidirect |
| 2. #28417946 | C2 | semidirect |
| 3. #28417939 | C2 | semidirect |
| 4. #28417937 | C2 | semidirect |
| 5. #28417936 | C2 | semidirect |
| 6. #28417935 | C2 | semidirect |
| 7. #28417932 | C2 | semidirect |
| 8. #28417930 | C2 | semidirect |
| 10. C4×C22⋊D467 | C2 | semidirect |
| 11. (C22⋊D467)⋊C4 | C2 | semidirect |
| 12. #28417912 | C2 | semidirect |
| 13. #28417909 | C2 | semidirect |
| 14. C2×C22⋊Dic467 | C2 | semidirect |
| 15. C2×C22⋊C4×C467 | C2 | semidirect |
| 16. C2×Dic934 | C22 | semidirect |
| 22. C2×C4×D467 | C22 | semidirect |
| 23. C4⋊Dic467 | C22 | semidirect |
| 24. C4⋊Dic467 | C22 | semidirect |
| 25. C4⋊Dic467 | C22 | semidirect |
| 26. Dic467⋊C4 | C22 | semidirect |
| 27. Dic467⋊C4 | C22 | semidirect |
| 28. Dic467⋊C4 | C22 | semidirect |
| 29. Dic467⋊C4 | C22 | semidirect |
| 30. Dic467⋊C4 | C22 | semidirect |
| 38. (C2×D467)⋊C4 | C22 | semidirect |
| 39. (C2×D467)⋊C4 | C22 | semidirect |
| 40. (C2×D467)⋊C4 | C22 | semidirect |
| 41. C4×Dic467 | C22 | semidirect |
| 42. C4×Dic467 | C22 | semidirect |
| 43. C4×Dic467 | C22 | semidirect |
| 110. C467 | #551 | semidirect |
| 126. C2×C22⋊C4 | D467 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #28417946 | 2 |
| #28417939 | 2 |
| #28417937 | 2 |
| #28417936 | 2 |
| #28417935 | 2 |
| #28417932 | 2 |
| #28417930 | 2 |
| #28417922 | 2 |
| C4×C22⋊D467 | 2 |
| (C22⋊D467)⋊C4 | 2 |
| #28417912 | 2 |
| #28417909 | 2 |
| C2×C22⋊Dic467 | 2 |
| C2×C22⋊C4×C467 | 2 |
| #551 | 467 |