Finite Group DatabasebetaFinite Group DatabasebetaOrder 29056.
548 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 131 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×#20300315 | C2 | semidirect |
| 2. #28409583 | C2 | semidirect |
| 3. C4×D4×D227 | C2 | semidirect |
| 4. #28409250 | C2 | semidirect |
| 5. #28409249 | C2 | semidirect |
| 6. #28409234 | C2 | semidirect |
| 7. #28409228 | C2 | semidirect |
| 8. #28409227 | C2 | semidirect |
| 9. #28409054 | C2 | semidirect |
| 10. #28409032 | C2 | semidirect |
| 11. #461×C227 | C2 | semidirect |
| 20. #20300285 | C22 | semidirect |
| 21. #20300277 | C22 | semidirect |
| 34. C4⋊(C227⋊C8) | C22 | semidirect |
| 35. Dic227⋊C8 | C22 | semidirect |
| 36. #20300212 | C22 | semidirect |
| 37. #20300210 | C22 | semidirect |
| 38. #20300208 | C22 | semidirect |
| 40. C4⋊Q8×C227 | C22 | semidirect |
| 42. C4⋊C8×C227 | C22 | semidirect |
| 43. #103×C227 | C22 | semidirect |
| 54. D4×D227 | D4 | semidirect |
| 146. C4×C227 | AGL(1,ℤ/8) | semidirect |
| 160. C227 | #3036 | semidirect |
| 168. #461 | D227 | semidirect |
| 182. C4⋊Q8 | C2×D227 | semidirect |
| 200. C4⋊C8 | C2×D227 | semidirect |
| 202. #103 | C2×D227 | semidirect |
| 311. C4 | #20300315 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20300315 | 2 |
| #28409583 | 2 |
| C4×D4×D227 | 2 |
| #28409250 | 2 |
| #28409249 | 2 |
| #28409234 | 2 |
| #28409228 | 2 |
| #28409227 | 2 |
| #28409054 | 2 |
| #28409032 | 2 |
| #461×C227 | 2 |
| #3036 | 227 |