Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
224 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 224 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 |
|---|---|---|
| 4. #27213104 | C2 | semidirect |
| 5. #27212907 | C2 | semidirect |
| 6. #27212900 | C2 | semidirect |
| 7. C2×#108×C211 | C2 | semidirect |
| 13. #20269902 | C4 | semidirect |
| 14. #20269902 | C4 | semidirect |
| 15. #20269899 | C4 | semidirect |
| 16. #20269899 | C4 | semidirect |
| 105. C211 | #1929 | semidirect |
| 107. C2×#108 | D211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20269903 | 2 |
| #27213143 | 2 |
| #27213114 | 2 |
| #27213104 | 2 |
| #27212907 | 2 |
| #27212900 | 2 |
| C2×#108×C211 | 2 |
| #1929 | 211 |