Finite Group DatabasebetaFinite Group DatabasebetaOrder 30656.
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. #29506375 | C2 | semidirect |
| 2. #29506375 | C2 | semidirect |
| 3. #29506368 | C2 | semidirect |
| 4. #29506366 | C2 | semidirect |
| 5. #29506365 | C2 | semidirect |
| 6. #29506364 | C2 | semidirect |
| 7. #29506361 | C2 | semidirect |
| 8. #29506359 | C2 | semidirect |
| 10. C4×C22⋊D479 | C2 | semidirect |
| 11. (C22⋊D479)⋊C4 | C2 | semidirect |
| 12. #29506341 | C2 | semidirect |
| 13. #29506338 | C2 | semidirect |
| 14. C2×C22⋊Dic479 | C2 | semidirect |
| 15. C2×C22⋊C4×C479 | C2 | semidirect |
| 16. C2×Dic958 | C22 | semidirect |
| 22. C2×C4×D479 | C22 | semidirect |
| 23. C4⋊Dic479 | C22 | semidirect |
| 24. C4⋊Dic479 | C22 | semidirect |
| 25. C4⋊Dic479 | C22 | semidirect |
| 26. Dic479⋊C4 | C22 | semidirect |
| 27. Dic479⋊C4 | C22 | semidirect |
| 28. Dic479⋊C4 | C22 | semidirect |
| 29. Dic479⋊C4 | C22 | semidirect |
| 30. Dic479⋊C4 | C22 | semidirect |
| 38. (C2×D479)⋊C4 | C22 | semidirect |
| 39. (C2×D479)⋊C4 | C22 | semidirect |
| 40. (C2×D479)⋊C4 | C22 | semidirect |
| 41. C4×Dic479 | C22 | semidirect |
| 42. C4×Dic479 | C22 | semidirect |
| 43. C4×Dic479 | C22 | semidirect |
| 110. C479 | #551 | semidirect |
| 126. C2×C22⋊C4 | D479 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #29506375 | 2 |
| #29506368 | 2 |
| #29506366 | 2 |
| #29506365 | 2 |
| #29506364 | 2 |
| #29506361 | 2 |
| #29506359 | 2 |
| #29506351 | 2 |
| C4×C22⋊D479 | 2 |
| (C22⋊D479)⋊C4 | 2 |
| #29506341 | 2 |
| #29506338 | 2 |
| C2×C22⋊Dic479 | 2 |
| C2×C22⋊C4×C479 | 2 |
| #551 | 479 |