Finite Group DatabasebetaFinite Group DatabasebetaOrder 29056.
612 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 197 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×#20300253 | C2 | semidirect |
| 4. #28408937 | C2 | semidirect |
| 6. #28408922 | C2 | semidirect |
| 7. #28408903 | C2 | semidirect |
| 8. #28408878 | C2 | semidirect |
| 9. #384×C227 | C2 | semidirect |
| 13. #20300276 | C4 | semidirect |
| 33. C2×Dic454 | C2×C4 | semidirect |
| 46. (C2×D227)⋊C4 | C2×C4 | semidirect |
| 57. C42×C227 | C2×C4 | semidirect |
| 111. C227 | #2326 | semidirect |
| 120. #384 | D227 | semidirect |
| 169. C42 | C4×D227 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20300276 | 2 |
| C2×#20300253 | 2 |
| C2×#20300250 | 2 |
| #28408937 | 2 |
| #28408933 | 2 |
| #28408922 | 2 |
| #28408903 | 2 |
| #28408878 | 2 |
| #384×C227 | 2 |
| #2326 | 227 |