Finite Group DatabasebetaFinite Group DatabasebetaOrder 29056.
360 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 3. C2×#20300213 | C2 | semidirect |
| 4. C2×#20300211 | C2 | semidirect |
| 6. #28408794 | C2 | semidirect |
| 7. #340×C227 | C2 | semidirect |
| 15. #20300268 | C4 | semidirect |
| 131. C227 | #1894 | semidirect |
| 139. #340 | D227 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16813867 | 2 |
| C2×#20300268 | 2 |
| C2×#20300213 | 2 |
| C2×#20300211 | 2 |
| #28408889 | 2 |
| #28408794 | 2 |
| #340×C227 | 2 |
| #1894 | 227 |