Finite Group DatabasebetaFinite Group DatabasebetaOrder 30656.
266 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 266 conjugacy classes of subgroups — too many to draw. Only its 111 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×#21440162 | C2 | semidirect |
| 2. #29506402 | C2 | direct (N × H) |
| 3. C2×#21440152 | C2 | semidirect |
| 4. C2×#21440150 | C2 | semidirect |
| 5. C2×#21440149 | C2 | semidirect |
| 6. C2×#21440147 | C2 | semidirect |
| 7. C22×C479⋊C8 | C2 | semidirect |
| 8. C2×#41×C479 | C2 | semidirect |
| 10. #21440162 | C22 | semidirect |
| 15. #21440152 | C22 | semidirect |
| 16. #21440150 | C22 | semidirect |
| 17. #21440149 | C22 | semidirect |
| 18. #21440147 | C22 | semidirect |
| 21. C2×C479⋊C8 | C22 | semidirect |
| 23. #41×C479 | C22 | semidirect |
| 66. C2×C479 | #135 | semidirect |
| 69. C479 | C2×#135 | semidirect |
| 72. C2×#41 | D479 | semidirect |
| 82. #41 | C2×D479 | semidirect |
| 137. C2 | #29506402 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#21440162 | 2 |
| #29506402 | 2 |
| C2×#21440152 | 2 |
| C2×#21440150 | 2 |
| C2×#21440149 | 2 |
| C2×#21440147 | 2 |
| C22×C479⋊C8 | 2 |
| C2×#41×C479 | 2 |
| C2×#135 | 479 |