Finite Group DatabasebetaFinite Group DatabasebetaOrder 29056.
224 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 75 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. C2×#20300224 | C2 | semidirect |
| 5. #28408987 | C2 | semidirect |
| 6. #28408792 | C2 | semidirect |
| 7. #336×C227 | C2 | semidirect |
| 14. #20300213 | C4 | semidirect |
| 15. #20300213 | C4 | semidirect |
| 16. #20300210 | C4 | semidirect |
| 17. #20300210 | C4 | semidirect |
| 105. C227 | #1929 | semidirect |
| 113. #336 | D227 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20300224 | 2 |
| C2×#20300216 | 2 |
| #28409029 | 2 |
| #28408998 | 2 |
| #28408987 | 2 |
| #28408792 | 2 |
| #336×C227 | 2 |
| #1929 | 227 |