Finite Group DatabasebetaFinite Group DatabasebetaOrder 29056.
500 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 165 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×#16813874 | C2 | semidirect |
| 4. #28409254 | C2 | direct (N × H) |
| 5. C2×C4⋊(C227⋊C8) | C2 | semidirect |
| 6. C2×#20300211 | C2 | semidirect |
| 8. C2×C4×Q8×C227 | C2 | semidirect |
| 12. C2×#16813874 | C22 | semidirect |
| 21. C4⋊(C227⋊C8) | C22 | semidirect |
| 22. #20300211 | C22 | semidirect |
| 26. C4×Q8×C227 | C22 | semidirect |
| 110. C2×C227 | #464 | semidirect |
| 115. C227 | C2×#464 | semidirect |
| 120. C2×C4×Q8 | D227 | semidirect |
| 137. C4×Q8 | C2×D227 | semidirect |
| 227. C2 | #28409254 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16813874 | 2 |
| C22×#16813871 | 2 |
| C2×#20300276 | 2 |
| #28409254 | 2 |
| C2×C4⋊(C227⋊C8) | 2 |
| C2×#20300211 | 2 |
| C2×#20300208 | 2 |
| C2×C4×Q8×C227 | 2 |
| C2×#464 | 227 |