Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
262 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 2. #27213194 | C2 | semidirect |
| 3. #27213169 | C2 | semidirect |
| 5. #27212916 | C2 | semidirect |
| 6. #27212905 | C2 | semidirect |
| 17. #20269904 | C4 | semidirect |
| 18. #20269904 | C4 | semidirect |
| 97. C211 | #1861 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27213913 | 2 |
| #27213194 | 2 |
| #27213169 | 2 |
| C2×#20269904 | 2 |
| #27212916 | 2 |
| #27212905 | 2 |
| #421×C211 | 2 |
| #1861 | 211 |