Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
416 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 153 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 |
|---|---|---|
| 4. #27212901 | C2 | semidirect |
| 5. #27212900 | C2 | semidirect |
| 6. #27212900 | C2 | semidirect |
| 7. #336×C211 | C2 | semidirect |
| 11. C2×#16809945 | C4 | semidirect |
| 16. C2×C8×D211 | C4 | semidirect |
| 108. C211 | #1729 | semidirect |
| 116. #336 | D211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16809945 | 2 |
| C22×C8×D211 | 2 |
| C2×#20269934 | 2 |
| #27212901 | 2 |
| #27212900 | 2 |
| #336×C211 | 2 |
| #1729 | 211 |