Finite Group DatabasebetaFinite Group DatabasebetaOrder 29056.
520 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 173 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. #28408936 | C2 | semidirect |
| 3. #28408926 | C2 | semidirect |
| 4. #28408920 | C2 | semidirect |
| 6. #28408905 | C2 | semidirect |
| 7. #28408904 | C2 | semidirect |
| 8. #28408896 | C2 | semidirect |
| 12. #20300275 | C4 | semidirect |
| 34. C2×Dic454 | C2×C4 | semidirect |
| 46. C22⋊Dic227 | C2×C4 | semidirect |
| 47. C22⋊Dic227 | C2×C4 | semidirect |
| 49. C4×Dic227 | C2×C4 | semidirect |
| 127. C227 | #2379 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20300275 | 2 |
| #28408936 | 2 |
| #28408926 | 2 |
| #28408920 | 2 |
| #28408912 | 2 |
| #28408905 | 2 |
| #28408904 | 2 |
| #28408896 | 2 |
| #386×C227 | 2 |
| #2379 | 227 |