Finite Group DatabasebetaFinite Group DatabasebetaOrder 29056.
142 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 142 conjugacy classes of subgroups — too many to draw. Only its 49 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 |
|---|---|---|
| 2. #28408859 | C2 | semidirect |
| 3. #28408857 | C2 | semidirect |
| 4. #28408832 | C2 | semidirect |
| 5. #28408832 | C2 | semidirect |
| 6. C22⋊(C227⋊C16) | C2 | semidirect |
| 7. #427×C227 | C2 | semidirect |
| 69. C227 | #2234 | semidirect |
| 72. #427 | D227 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #28409268 | 2 |
| #28408859 | 2 |
| #28408857 | 2 |
| #28408832 | 2 |
| C22⋊(C227⋊C16) | 2 |
| #427×C227 | 2 |
| #2234 | 227 |