Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
360 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 119 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. M16×Dic211 | C2 | semidirect |
| 4. #27212914 | C2 | semidirect |
| 13. #20269894 | C4 | semidirect |
| 18. #100×C211 | C4 | semidirect |
| 26. #16809946 | C2×C4 | semidirect |
| 39. M16×C211 | C2×C4 | semidirect |
| 79. Dic211 | #100 | direct (N × H) |
| 86. C211 | C4×#100 | semidirect |
| 103. #100 | Dic211 | direct (N × H) |
| 121. M16 | C2×Dic211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×Dic211 | 2 |
| C2×#20269894 | 2 |
| M16×Dic211 | 2 |
| #27212914 | 2 |
| C2×#100×C211 | 2 |
| C4×#100 | 211 |