Finite Group DatabasebetaFinite Group DatabasebetaOrder 29056.
400 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 181 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. #28409094 | C2 | semidirect |
| 3. #28409083 | C2 | semidirect |
| 4. #28409060 | C2 | semidirect |
| 6. C2×C4×C227⋊C8 | C2 | semidirect |
| 7. C4×M16×C227 | C2 | semidirect |
| 77. C227 | #2922 | semidirect |
| 84. C4×M16 | D227 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#16813884 | 2 |
| #28409094 | 2 |
| #28409083 | 2 |
| #28409060 | 2 |
| #28409000 | 2 |
| C2×C4×C227⋊C8 | 2 |
| C4×M16×C227 | 2 |
| #2922 | 227 |