Finite Group DatabasebetaFinite Group DatabasebetaOrder 29056.
120 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 120 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 |
|---|---|---|
| 27. C227⋊C16 | Q8 | semidirect |
| 31. C16×C227 | Q8 | semidirect |
| 55. C227 | #2255 | semidirect |
| 87. C16 | Dic454 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #28409436 | 2 |
| #28409433 | 2 |
| #28408859 | 2 |
| #28408858 | 2 |
| #28408857 | 2 |
| #28408807 | 2 |
| #367×C227 | 2 |
| #2255 | 227 |