Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
282 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 282 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 28. C4⋊Dic211 | Q8 | semidirect |
| 35. C2×C8×C211 | Q8 | semidirect |
| 80. C211 | #2057 | semidirect |
| 109. C2×C8 | Dic422 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20269977 | 2 |
| C2×#20269911 | 2 |
| #27213044 | 2 |
| #27212909 | 2 |
| #336×C211 | 2 |
| #2057 | 211 |