Finite Group DatabasebetaFinite Group DatabasebetaOrder 30656.
234 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 103 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. #29506376 | C2 | semidirect |
| 2. #29506374 | C2 | semidirect |
| 3. #29506370 | C2 | semidirect |
| 4. #29506365 | C2 | semidirect |
| 5. #29506361 | C2 | semidirect |
| 7. C4×Dic958 | C2 | semidirect |
| 8. C4×D1916 | C2 | semidirect |
| 9. C4×C22⋊D479 | C2 | semidirect |
| 10. #29506339 | C2 | semidirect |
| 11. C2×C42×C479 | C2 | semidirect |
| 74. C479 | #529 | semidirect |
| 86. C2×C42 | D479 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #29506376 | 2 |
| #29506374 | 2 |
| #29506370 | 2 |
| #29506365 | 2 |
| #29506361 | 2 |
| #29506356 | 2 |
| C4×Dic958 | 2 |
| C4×D1916 | 2 |
| C4×C22⋊D479 | 2 |
| #29506339 | 2 |
| C2×C42×C479 | 2 |
| #529 | 479 |