Finite Group DatabasebetaFinite Group DatabasebetaOrder 29056.
548 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 145 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. #28409582 | C2 | semidirect |
| 3. C2×C4×D908 | C2 | semidirect |
| 4. #28409248 | C2 | semidirect |
| 5. #28409238 | C2 | semidirect |
| 6. #28409228 | C2 | semidirect |
| 7. #28409034 | C2 | semidirect |
| 8. #423×C227 | C2 | semidirect |
| 15. #20300288 | C22 | semidirect |
| 16. #20300285 | C22 | semidirect |
| 17. #20300276 | C22 | semidirect |
| 28. #20300213 | C22 | semidirect |
| 29. #20300210 | C22 | semidirect |
| 32. C4⋊C8×C227 | C22 | semidirect |
| 33. C4⋊C8×C227 | C22 | semidirect |
| 42. C2×D908 | D4 | semidirect |
| 118. C4×C227 | AGL(1,ℤ/8) | semidirect |
| 129. C227 | #3036 | semidirect |
| 137. #423 | D227 | semidirect |
| 160. C4⋊C8 | C2×D227 | semidirect |
| 161. C4⋊C8 | C2×D227 | semidirect |
| 250. C4 | #20300316 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20300316 | 2 |
| #28409582 | 2 |
| C2×C4×D908 | 2 |
| #28409248 | 2 |
| #28409238 | 2 |
| #28409228 | 2 |
| #28409034 | 2 |
| #423×C227 | 2 |
| #3036 | 227 |