Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
412 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 119 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. C22⋊C4×Dic211 | C2 | semidirect |
| 4. #27212912 | C2 | semidirect |
| 6. C23×Dic211 | C4 | semidirect |
| 10. C2×C4⋊Dic211 | C4 | semidirect |
| 11. C2×C22⋊Dic211 | C4 | semidirect |
| 15. C2×C4×Dic211 | C4 | semidirect |
| 16. #20269892 | C4 | semidirect |
| 20. #99×C211 | C4 | semidirect |
| 36. C22⋊Dic211 | C2×C4 | semidirect |
| 49. C22⋊C4×C211 | C2×C4 | semidirect |
| 72. C23×C211 | C42 | semidirect |
| 85. C2×C4×C211 | C42 | semidirect |
| 110. Dic211 | #99 | direct (N × H) |
| 119. C211 | C4×#99 | semidirect |
| 139. #99 | Dic211 | direct (N × H) |
| 166. C22⋊C4 | C2×Dic211 | semidirect |
| 176. C23 | C4×Dic211 | semidirect |
| 205. C2×C4 | C4×Dic211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×Dic211 | 2 |
| C2×#20269892 | 2 |
| C22⋊C4×Dic211 | 2 |
| #27212912 | 2 |
| C2×#99×C211 | 2 |
| C4×#99 | 211 |