Finite Group DatabasebetaFinite Group DatabasebetaOrder 29056.
216 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 71 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 |
|---|---|---|
| 4. M16×Dic227 | C2 | semidirect |
| 5. #28408803 | C2 | semidirect |
| 6. #28408793 | C2 | semidirect |
| 7. #430×C227 | C2 | semidirect |
| 15. #20300206 | C4 | semidirect |
| 16. #20300204 | C4 | semidirect |
| 95. C227 | #1932 | semidirect |
| 97. #430 | D227 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #28409048 | 2 |
| C2×#20300214 | 2 |
| #28409014 | 2 |
| M16×Dic227 | 2 |
| #28408803 | 2 |
| #28408793 | 2 |
| #430×C227 | 2 |
| #1932 | 227 |