Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
164 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 61 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 |
|---|---|---|
| 8. #20269888 | C4 | semidirect |
| 11. C4⋊C8×C211 | C4 | semidirect |
| 59. C211 | #1285 | semidirect |
| 68. C4⋊C8 | Dic211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27213203 | 2 |
| C4×C4⋊Dic211 | 2 |
| #432×C211 | 2 |
| #1285 | 211 |