Finite Group DatabasebetaFinite Group DatabasebetaOrder 29056.
146 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 146 conjugacy classes of subgroups — too many to draw. Only its 57 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. #28409150 | C2 | semidirect |
| 3. #28408861 | C2 | semidirect |
| 4. #28408839 | C2 | semidirect |
| 5. #28408838 | C2 | semidirect |
| 6. C4×C227⋊C16 | C2 | semidirect |
| 7. #443×C227 | C2 | semidirect |
| 10. #20300234 | C4 | semidirect |
| 11. #20300232 | C4 | semidirect |
| 12. #20300231 | C4 | semidirect |
| 13. #20300229 | C4 | semidirect |
| 71. C227 | #2178 | semidirect |
| 75. #443 | D227 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #28409462 | 2 |
| #28409150 | 2 |
| #28408861 | 2 |
| #28408839 | 2 |
| #28408838 | 2 |
| C4×C227⋊C16 | 2 |
| #443×C227 | 2 |
| #2178 | 227 |