Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
260 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 101 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 |
|---|---|---|
| 33. M16×C211 | Q8 | semidirect |
| 72. C211 | #1997 | semidirect |
| 101. M16 | Dic422 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20269977 | 2 |
| #27213170 | 2 |
| #27212914 | 2 |
| C4×M16×C211 | 2 |
| #1997 | 211 |