Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
216 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 216 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 |
|---|---|---|
| 1. #27213195 | C2 | semidirect |
| 2. #27213194 | C2 | semidirect |
| 3. #27213194 | C2 | semidirect |
| 6. C211⋊#338 | C2 | semidirect |
| 85. C211 | #2069 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27213195 | 2 |
| #27213194 | 2 |
| C2×#20269894 | 2 |
| C211⋊#338 | 2 |
| C2×#100×C211 | 2 |
| #2069 | 211 |