Finite Group DatabasebetaFinite Group DatabasebetaOrder 29056.
312 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 16. C2×Q16×C227 | C4 | semidirect |
| 43. C2×Dic227 | Q16 | semidirect |
| 77. C227 | #1969 | semidirect |
| 87. C2×Q16 | Dic227 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20300222 | 2 |
| C2×#20300212 | 2 |
| C2×C8×Dic227 | 2 |
| #28408939 | 2 |
| C22×Q16×C227 | 2 |
| #1969 | 227 |