Finite Group DatabasebetaFinite Group DatabasebetaOrder 29056.
218 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 218 conjugacy classes of subgroups — too many to draw. Only its 53 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. #28409411 | C2 | semidirect |
| 3. #28409319 | C2 | semidirect |
| 4. #28408780 | C2 | semidirect |
| 5. D4⋊(C227⋊C8) | C2 | semidirect |
| 6. #28408759 | C2 | semidirect |
| 7. #476×C227 | C2 | semidirect |
| 92. C227 | #1634 | semidirect |
| 97. #476 | D227 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #28409747 | 2 |
| #28409411 | 2 |
| #28409319 | 2 |
| #28408780 | 2 |
| D4⋊(C227⋊C8) | 2 |
| #28408759 | 2 |
| #476×C227 | 2 |
| #1634 | 227 |