Finite Group DatabasebetaFinite Group DatabasebetaOrder 29056.
548 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 153 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×#20300314 | C2 | semidirect |
| 2. #28409582 | C2 | semidirect |
| 3. #28409247 | C2 | semidirect |
| 4. #28409237 | C2 | semidirect |
| 5. #28409227 | C2 | semidirect |
| 6. #28409056 | C2 | semidirect |
| 7. #28409031 | C2 | semidirect |
| 8. C2×C4×D4×C227 | C2 | semidirect |
| 14. #20300288 | C22 | semidirect |
| 15. #20300285 | C22 | semidirect |
| 16. #20300276 | C22 | semidirect |
| 21. C4⋊(C227⋊C8) | C22 | semidirect |
| 22. C4⋊(C227⋊C8) | C22 | semidirect |
| 23. #20300211 | C22 | semidirect |
| 24. #20300208 | C22 | semidirect |
| 53. C2×D4×C227 | D4 | semidirect |
| 119. C4×C227 | AGL(1,ℤ/8) | semidirect |
| 129. C227 | #3036 | semidirect |
| 133. C2×C4×D4 | D227 | semidirect |
| 174. C2×D4 | D908 | semidirect |
| 250. C4 | #20300314 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20300314 | 2 |
| #28409582 | 2 |
| #28409247 | 2 |
| #28409237 | 2 |
| #28409227 | 2 |
| #28409056 | 2 |
| #28409031 | 2 |
| C2×C4×D4×C227 | 2 |
| #3036 | 227 |