Finite Group DatabasebetaFinite Group DatabasebetaOrder 30592.
688 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 688 conjugacy classes of subgroups — too many to draw. Only its 173 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 |
|---|---|---|
| 2. #29504672 | C2 | semidirect |
| 3. #29504666 | C2 | semidirect |
| 4. #29504660 | C2 | semidirect |
| 5. #29504648 | C2 | semidirect |
| 6. #29504628 | C2 | semidirect |
| 7. #379×C239 | C2 | semidirect |
| 9. C22×C4×D239 | C22 | semidirect |
| 10. #21439929 | C4 | semidirect |
| 11. C2×Dic239⋊C4 | C22 | semidirect |
| 15. C2×(C2×D239)⋊C4 | C22 | semidirect |
| 16. C2×C4×Dic239 | C22 | semidirect |
| 17. C239⋊#95 | C22 | semidirect |
| 18. C239⋊#95 | C22 | semidirect |
| 33. C22⋊Dic239 | C2×C4 | semidirect |
| 38. C24×C239 | C2×C4 | semidirect |
| 95. C239 | #2375 | semidirect |
| 103. #379 | D239 | semidirect |
| 121. C24 | C4×D239 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#21439929 | 2 |
| #29504672 | 2 |
| #29504666 | 2 |
| #29504660 | 2 |
| #29504648 | 2 |
| #29504628 | 2 |
| #379×C239 | 2 |
| #2375 | 239 |