Finite Group DatabasebetaFinite Group DatabasebetaOrder 29056.
556 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 556 conjugacy classes of subgroups — too many to draw. Only its 189 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×#20300280 | C2 | semidirect |
| 2. #28408930 | C2 | semidirect |
| 3. #28408916 | C2 | semidirect |
| 5. #28408898 | C2 | semidirect |
| 74. C22×C227 | #125 | semidirect |
| 92. C227 | #2851 | semidirect |
| 167. C22 | #20300280 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20300280 | 2 |
| #28408930 | 2 |
| #28408916 | 2 |
| #28408905 | 2 |
| #28408898 | 2 |
| #28408892 | 2 |
| C22×C42×C227 | 2 |
| #2851 | 227 |