Finite Group DatabasebetaFinite Group DatabasebetaOrder 29056.
648 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 648 conjugacy classes of subgroups — too many to draw. Only its 157 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. C22×D1816 | C2 | semidirect |
| 2. C22×#16813869 | C2 | semidirect |
| 3. C2×#20300284 | C2 | semidirect |
| 4. C2×#20300250 | C2 | semidirect |
| 5. #28409226 | C2 | direct (N × H) |
| 6. C2×Dic227⋊C8 | C2 | semidirect |
| 7. C2×#20300208 | C2 | semidirect |
| 8. C2×#102×C227 | C2 | semidirect |
| 15. C2×D1816 | C22 | semidirect |
| 17. C2×#16813869 | C22 | semidirect |
| 20. #20300284 | C22 | semidirect |
| 22. #20300250 | C22 | semidirect |
| 25. Dic227⋊C8 | C22 | semidirect |
| 26. #20300208 | C22 | semidirect |
| 30. #102×C227 | C22 | semidirect |
| 38. C2×D908 | D4 | semidirect |
| 80. D908 | C2×D4 | semidirect |
| 84. C2×Dic227 | D8 | semidirect |
| 125. Dic227 | C2×D8 | semidirect |
| 127. C2×C227 | #459 | semidirect |
| 133. C227 | C2×#459 | semidirect |
| 142. C2×#102 | D227 | semidirect |
| 164. #102 | C2×D227 | semidirect |
| 263. C2 | #28409226 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D1816 | 2 |
| C22×#16813869 | 2 |
| C2×#20300284 | 2 |
| C2×#20300250 | 2 |
| #28409226 | 2 |
| C2×Dic227⋊C8 | 2 |
| C2×#20300208 | 2 |
| C2×#102×C227 | 2 |
| C2×#459 | 227 |