Finite Group DatabasebetaFinite Group DatabasebetaOrder 30592.
300 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 4. #29504728 | C2 | semidirect |
| 5. C2×C4×C239⋊C8 | C2 | semidirect |
| 6. #29504536 | C2 | semidirect |
| 7. #339×C239 | C2 | semidirect |
| 10. #21439968 | C4 | semidirect |
| 16. #21439888 | C4 | semidirect |
| 17. #21439883 | C4 | semidirect |
| 18. #21439880 | C4 | semidirect |
| 98. C239 | #1764 | semidirect |
| 106. #339 | D239 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#21439968 | 2 |
| C2×#21439888 | 2 |
| #29504766 | 2 |
| #29504728 | 2 |
| C2×C4×C239⋊C8 | 2 |
| #29504536 | 2 |
| #339×C239 | 2 |
| #1764 | 239 |