Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
222 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 222 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. #27213174 | C2 | semidirect |
| 4. C2×#20269888 | C2 | semidirect |
| 5. #27212910 | C2 | semidirect |
| 6. #27212906 | C2 | semidirect |
| 13. #20269901 | C4 | semidirect |
| 14. #20269898 | C4 | semidirect |
| 90. C211 | #1938 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27213174 | 2 |
| #27213142 | 2 |
| #27213113 | 2 |
| C2×#20269888 | 2 |
| #27212910 | 2 |
| #27212906 | 2 |
| C2×#104×C211 | 2 |
| #1938 | 211 |