Finite Group DatabasebetaFinite Group DatabasebetaOrder 29056.
126 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 126 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 |
|---|---|---|
| 33. C16×C227 | Q8 | semidirect |
| 59. C227 | #2183 | semidirect |
| 93. C16 | Dic454 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C8×Dic454 | 2 |
| C4⋊(C227⋊C16) | 2 |
| Dic227⋊C16 | 2 |
| #28408807 | 2 |
| C16×Dic227 | 2 |
| #346×C227 | 2 |
| #2183 | 227 |