Finite Group DatabasebetaFinite Group DatabasebetaOrder 29056.
548 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 135 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×#20300316 | C2 | semidirect |
| 2. C2×#20300313 | C2 | semidirect |
| 3. #28409578 | C2 | semidirect |
| 4. C2×#20300250 | C2 | semidirect |
| 5. #28409250 | C2 | semidirect |
| 6. #28409246 | C2 | semidirect |
| 7. #28409236 | C2 | semidirect |
| 8. #28409226 | C2 | semidirect |
| 9. #28409055 | C2 | semidirect |
| 10. #28409031 | C2 | semidirect |
| 11. #417×C227 | C2 | semidirect |
| 22. #20300286 | C22 | semidirect |
| 23. #20300284 | C22 | semidirect |
| 24. #20300277 | C22 | semidirect |
| 25. #20300275 | C22 | semidirect |
| 36. Dic227⋊C8 | C22 | semidirect |
| 37. Dic227⋊C8 | C22 | semidirect |
| 38. #20300211 | C22 | semidirect |
| 39. #20300208 | C22 | semidirect |
| 43. #103×C227 | C22 | semidirect |
| 44. #102×C227 | C22 | semidirect |
| 51. C2×D908 | D4 | semidirect |
| 158. Dic227 | AGL(1,ℤ/8) | semidirect |
| 166. C227 | #3036 | semidirect |
| 178. #417 | D227 | semidirect |
| 209. #103 | C2×D227 | semidirect |
| 211. #102 | C2×D227 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20300316 | 2 |
| C2×#20300313 | 2 |
| #28409578 | 2 |
| C2×#20300250 | 2 |
| #28409250 | 2 |
| #28409246 | 2 |
| #28409236 | 2 |
| #28409226 | 2 |
| #28409055 | 2 |
| #28409031 | 2 |
| #417×C227 | 2 |
| #3036 | 227 |