Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
110 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 110 conjugacy classes of subgroups — too many to draw. Only its 47 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 |
|---|---|---|
| 2. C4⋊(C211⋊C16) | C2 | semidirect |
| 3. C4×C16×C211 | C2 | semidirect |
| 25. D844 | C16 | semidirect |
| 50. C211 | D4⋊C16 | semidirect |
| 54. C4×C16 | D211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C8×D844 | 2 |
| C4⋊(C211⋊C16) | 2 |
| C4×C16×C211 | 2 |
| D4⋊C16 | 211 |