Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
300 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 115 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 |
|---|---|---|
| 11. #20269976 | C4 | semidirect |
| 31. C2×C211⋊C8 | Q8 | semidirect |
| 46. C2×C8×C211 | Q8 | semidirect |
| 103. C211 | #1990 | semidirect |
| 141. C2×C8 | Dic422 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20269976 | 2 |
| C2×C8×Dic211 | 2 |
| #27213015 | 2 |
| #27212909 | 2 |
| #27212908 | 2 |
| #340×C211 | 2 |
| #1990 | 211 |