Finite Group DatabasebetaFinite Group DatabasebetaOrder 30656.
234 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 101 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. #29506373 | C2 | semidirect |
| 3. #29506369 | C2 | semidirect |
| 4. #29506364 | C2 | semidirect |
| 5. #29506362 | C2 | semidirect |
| 7. C4×Dic958 | C2 | semidirect |
| 8. C4×C22⋊D479 | C2 | semidirect |
| 9. #29506341 | C2 | semidirect |
| 10. C42×D479 | C2 | semidirect |
| 11. C4×D4×C479 | C2 | semidirect |
| 74. C479 | #529 | semidirect |
| 84. C4×D4 | D479 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #29506375 | 2 |
| #29506373 | 2 |
| #29506369 | 2 |
| #29506364 | 2 |
| #29506362 | 2 |
| #29506353 | 2 |
| C4×Dic958 | 2 |
| C4×C22⋊D479 | 2 |
| #29506341 | 2 |
| C42×D479 | 2 |
| C4×D4×C479 | 2 |
| #529 | 479 |