Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
232 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 75 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 |
|---|---|---|
| 1. #27213188 | C2 | semidirect |
| 5. #27213101 | C2 | semidirect |
| 6. #27212914 | C2 | semidirect |
| 7. #341×C211 | C2 | semidirect |
| 18. #20269893 | C4 | semidirect |
| 100. C211 | #1931 | semidirect |
| 108. #341 | D211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27213188 | 2 |
| #27213152 | 2 |
| C2×#20269899 | 2 |
| C2×#20269893 | 2 |
| #27213101 | 2 |
| #27212914 | 2 |
| #341×C211 | 2 |
| #1931 | 211 |