Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
348 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 137 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 |
|---|---|---|
| 2. C2×#20269887 | C2 | semidirect |
| 3. C2×C8×Dic211 | C2 | semidirect |
| 5. #27212900 | C2 | semidirect |
| 6. #27212900 | C2 | semidirect |
| 10. C2×#16809946 | C4 | semidirect |
| 22. C22⋊C8×C211 | C4 | semidirect |
| 57. C2×Dic211 | M16 | semidirect |
| 59. C211⋊C8 | C22⋊C4 | semidirect |
| 104. C211 | #1753 | semidirect |
| 124. C22⋊C8 | Dic211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16809946 | 2 |
| C2×#20269887 | 2 |
| C2×C8×Dic211 | 2 |
| C4×C22⋊Dic211 | 2 |
| #27212900 | 2 |
| C2×C22⋊C8×C211 | 2 |
| #1753 | 211 |