Finite Group DatabasebetaFinite Group DatabasebetaOrder 29056.
142 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 142 conjugacy classes of subgroups — too many to draw. Only its 45 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. #28409069 | C2 | semidirect |
| 3. #28408859 | C2 | semidirect |
| 4. #28408858 | C2 | semidirect |
| 5. #28408833 | C2 | semidirect |
| 6. (C2×D227)⋊C16 | C2 | semidirect |
| 7. #357×C227 | C2 | semidirect |
| 69. C227 | #2234 | semidirect |
| 76. #357 | D227 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #28409265 | 2 |
| #28409069 | 2 |
| #28408859 | 2 |
| #28408858 | 2 |
| #28408833 | 2 |
| (C2×D227)⋊C16 | 2 |
| #357×C227 | 2 |
| #2234 | 227 |