Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
292 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 105 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. #27213102 | C2 | semidirect |
| 5. C2×#20269888 | C2 | semidirect |
| 6. #27212910 | C2 | semidirect |
| 7. #339×C211 | C2 | semidirect |
| 10. #20269985 | C4 | semidirect |
| 16. #20269905 | C4 | semidirect |
| 17. #20269900 | C4 | semidirect |
| 18. #20269897 | C4 | semidirect |
| 98. C211 | #1765 | semidirect |
| 106. #339 | D211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20269985 | 2 |
| C2×#20269905 | 2 |
| #27213140 | 2 |
| #27213102 | 2 |
| C2×#20269888 | 2 |
| #27212910 | 2 |
| #339×C211 | 2 |
| #1765 | 211 |