Finite Group DatabasebetaFinite Group DatabasebetaOrder 29056.
612 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 205 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. C2×C4×Dic454 | C2 | semidirect |
| 3. #28408937 | C2 | semidirect |
| 5. #28408920 | C2 | semidirect |
| 6. #28408905 | C2 | semidirect |
| 7. #28408901 | C2 | semidirect |
| 8. #28408878 | C2 | semidirect |
| 11. #20300275 | C4 | semidirect |
| 32. C2×Dic454 | C2×C4 | semidirect |
| 41. C22⋊Dic227 | C2×C4 | semidirect |
| 44. C4×Dic227 | C2×C4 | semidirect |
| 111. C227 | #2326 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20300275 | 2 |
| C2×C4×Dic454 | 2 |
| #28408937 | 2 |
| #28408935 | 2 |
| #28408920 | 2 |
| #28408905 | 2 |
| #28408901 | 2 |
| #28408878 | 2 |
| C2×C4×D4×C227 | 2 |
| #2326 | 227 |