Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
156 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 156 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 |
|---|---|---|
| 36. Q8×C211 | Q16 | semidirect |
| 57. C211 | #1670 | semidirect |
| 92. Q8 | Dic844 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27213526 | 2 |
| #27213431 | 2 |
| #27212899 | 2 |
| #27212893 | 2 |
| C8×Q8×C211 | 2 |
| #1670 | 211 |