Finite Group DatabasebetaFinite Group DatabasebetaOrder 29056.
206 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 206 conjugacy classes of subgroups — too many to draw. Only its 47 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×#20300234 | C2 | semidirect |
| 3. #28409304 | C2 | semidirect |
| 4. #28408849 | C2 | semidirect |
| 5. #28408839 | C2 | semidirect |
| 6. #28408817 | C2 | semidirect |
| 7. #510×C227 | C2 | semidirect |
| 88. C227 | #2195 | semidirect |
| 91. #510 | D227 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #28409846 | 2 |
| C2×#20300234 | 2 |
| #28409304 | 2 |
| #28408849 | 2 |
| #28408839 | 2 |
| #28408817 | 2 |
| #510×C227 | 2 |
| #2195 | 227 |