Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
152 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 63 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 |
|---|---|---|
| 48. C211⋊C8 | Q16 | semidirect |
| 71. C211 | #1591 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27213277 | 2 |
| #27213273 | 2 |
| C4×#16809952 | 2 |
| #27212898 | 2 |
| #27212878 | 2 |
| C8×C211⋊C8 | 2 |
| Q8⋊C8×C211 | 2 |
| #1591 | 211 |