Finite Group DatabasebetaFinite Group DatabasebetaOrder 29056.
184 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 53 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×#20300234 | C2 | semidirect |
| 2. C2×#20300233 | C2 | semidirect |
| 4. #28409417 | C2 | semidirect |
| 5. #28409415 | C2 | semidirect |
| 6. C16×Dic227 | C2 | semidirect |
| 7. C2×SD32×C227 | C2 | semidirect |
| 75. C227 | #2249 | semidirect |
| 79. C2×SD32 | D227 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20300234 | 2 |
| C2×#20300233 | 2 |
| C2×#20300229 | 2 |
| #28409417 | 2 |
| #28409415 | 2 |
| C16×Dic227 | 2 |
| C2×SD32×C227 | 2 |
| #2249 | 227 |