Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
168 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 71 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 |
|---|---|---|
| 1. #27213277 | C2 | semidirect |
| 3. #27212899 | C2 | semidirect |
| 4. Q8⋊(C211⋊C8) | C2 | semidirect |
| 6. #27212868 | C2 | semidirect |
| 77. C211 | #1585 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27213277 | 2 |
| D4×C211⋊C8 | 2 |
| #27212899 | 2 |
| Q8⋊(C211⋊C8) | 2 |
| D4⋊(C211⋊C8) | 2 |
| #27212868 | 2 |
| C4×SD16×C211 | 2 |
| #1585 | 211 |