Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
136 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 77 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 |
|---|---|---|
| 8. C2×C211⋊C16 | C4 | semidirect |
| 13. M32×C211 | C4 | semidirect |
| 56. C211 | #1379 | semidirect |
| 65. M32 | Dic211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C211⋊C16 | 2 |
| #27213101 | 2 |
| C2×M32×C211 | 2 |
| #1379 | 211 |