Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
402 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 3. C2×#20269902 | C2 | semidirect |
| 4. #27213051 | C2 | semidirect |
| 5. #27212908 | C2 | semidirect |
| 6. #27212900 | C2 | semidirect |
| 12. C2×#16809950 | C4 | semidirect |
| 31. C2×Dic422 | C2×C4 | semidirect |
| 42. C2×C211⋊C8 | C2×C4 | semidirect |
| 78. C2×Dic211 | SD16 | semidirect |
| 133. C211 | #1877 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16809950 | 2 |
| C2×D4×Dic211 | 2 |
| C2×#20269902 | 2 |
| #27213051 | 2 |
| #27212908 | 2 |
| #27212900 | 2 |
| C2×#102×C211 | 2 |
| #1877 | 211 |