Finite Group DatabasebetaFinite Group DatabasebetaOrder 29056.
598 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 598 conjugacy classes of subgroups — too many to draw. Only its 97 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. C22×C22⋊Dic227 | C2 | semidirect |
| 3. C2×#20300202 | C2 | semidirect |
| 4. #28408798 | C2 | semidirect |
| 5. #379×C227 | C2 | semidirect |
| 6. C22×C22⋊D227 | C4 | semidirect |
| 14. C2×C22⋊Dic227 | C4 | semidirect |
| 21. C23×D227 | C2×C4 | semidirect |
| 32. C22×Dic227 | C2×C4 | semidirect |
| 33. C22×Dic227 | C2×C4 | semidirect |
| 40. C22⋊Dic227 | D4 | semidirect |
| 108. C22×C227 | #99 | semidirect |
| 130. C227 | #1898 | semidirect |
| 135. #379 | D227 | semidirect |
| 242. C22 | #20300202 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20300257 | 2 |
| C22×C22⋊Dic227 | 2 |
| C2×#20300202 | 2 |
| #28408798 | 2 |
| #379×C227 | 2 |
| #1898 | 227 |