Finite Group DatabasebetaFinite Group DatabasebetaOrder 30592.
324 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 89 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. #29504789 | C2 | semidirect |
| 3. #29504778 | C2 | semidirect |
| 4. C2×#21439876 | C2 | semidirect |
| 5. #29504544 | C2 | semidirect |
| 6. C239⋊#338 | C2 | semidirect |
| 7. #568×C239 | C2 | semidirect |
| 11. C2×#16838535 | C4 | semidirect |
| 12. C2×#16838533 | C4 | semidirect |
| 112. C239 | #1903 | semidirect |
| 115. #568 | D239 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#21439985 | 2 |
| #29504789 | 2 |
| #29504778 | 2 |
| C2×#21439876 | 2 |
| #29504544 | 2 |
| C239⋊#338 | 2 |
| #568×C239 | 2 |
| #1903 | 239 |