Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
208 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 208 conjugacy classes of subgroups — too many to draw. Only its 65 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 |
|---|---|---|
| 90. C211 | #2064 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20269912 | 2 |
| #27213186 | 2 |
| #27213174 | 2 |
| #27213156 | 2 |
| C2×#20269900 | 2 |
| C2×#20269895 | 2 |
| #343×C211 | 2 |
| #2064 | 211 |