Finite Group DatabasebetaFinite Group DatabasebetaOrder 30592.
290 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 97 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. C2×#21439893 | C2 | semidirect |
| 5. #29504534 | C2 | semidirect |
| 6. #29504527 | C2 | semidirect |
| 7. C4×C4⋊C4×C239 | C2 | semidirect |
| 16. #21439880 | C4 | semidirect |
| 118. C239 | #1925 | semidirect |
| 124. C4×C4⋊C4 | D239 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#21439893 | 2 |
| C2×#21439880 | 2 |
| #29504674 | 2 |
| #29504534 | 2 |
| #29504527 | 2 |
| C4×C4⋊C4×C239 | 2 |
| #1925 | 239 |