Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
212 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 73 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 |
|---|---|---|
| 3. #27212887 | C2 | semidirect |
| 72. C211 | #1528 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20269969 | 2 |
| C4×#16809946 | 2 |
| #27212887 | 2 |
| #432×C211 | 2 |
| #1528 | 211 |