Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
270 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 270 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×#20269913 | C2 | semidirect |
| 3. #27213172 | C2 | semidirect |
| 6. #27212906 | C2 | semidirect |
| 7. #336×C211 | C2 | semidirect |
| 20. #20269902 | C4 | semidirect |
| 21. #20269902 | C4 | semidirect |
| 22. #20269899 | C4 | semidirect |
| 23. #20269899 | C4 | semidirect |
| 109. C211 | #1866 | semidirect |
| 117. #336 | D211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20269983 | 2 |
| C2×#20269913 | 2 |
| #27213172 | 2 |
| C2×#20269905 | 2 |
| #27213143 | 2 |
| #27212906 | 2 |
| #336×C211 | 2 |
| #1866 | 211 |