Finite Group DatabasebetaFinite Group DatabasebetaOrder 29056.
390 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 89 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. C2×#20300211 | C2 | semidirect |
| 6. #28408787 | C2 | semidirect |
| 7. #391×C227 | C2 | semidirect |
| 125. C227 | #2015 | semidirect |
| 132. #391 | D227 | semidirect |
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 |
| C2×#20300211 | 2 |
| C2×#20300208 | 2 |
| #28408787 | 2 |
| #391×C227 | 2 |
| #2015 | 227 |