Finite Group DatabasebetaFinite Group DatabasebetaOrder 29056.
392 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 91 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 |
|---|---|---|
| 1. C22×#16813874 | C2 | semidirect |
| 4. C2×#20300213 | C2 | semidirect |
| 6. #28408794 | C2 | semidirect |
| 7. C2×#103×C227 | C2 | semidirect |
| 75. C22×D227 | Q16 | semidirect |
| 143. C227 | #2001 | semidirect |
| 149. C2×#103 | D227 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16813874 | 2 |
| C2×#20300268 | 2 |
| C2×#20300264 | 2 |
| C2×#20300213 | 2 |
| C2×(C2×D227)⋊C8 | 2 |
| #28408794 | 2 |
| C2×#103×C227 | 2 |
| #2001 | 227 |