Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
324 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 83 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. C2×#20269983 | C2 | semidirect |
| 3. C2×#20269905 | C2 | semidirect |
| 4. C2×#20269905 | C2 | semidirect |
| 5. #27213112 | C2 | semidirect |
| 6. #27212911 | C2 | semidirect |
| 7. #336×C211 | C2 | semidirect |
| 12. C2×Dic844 | C4 | semidirect |
| 13. C2×#16809951 | C4 | semidirect |
| 14. C2×#16809951 | C4 | semidirect |
| 15. C2×D1688 | C4 | semidirect |
| 130. C211 | #1876 | semidirect |
| 138. #336 | D211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20269999 | 2 |
| C2×#20269983 | 2 |
| C2×#20269905 | 2 |
| #27213112 | 2 |
| #27212911 | 2 |
| #336×C211 | 2 |
| #1876 | 211 |