Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
248 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 4. #27212878 | C2 | semidirect |
| 5. Q8⋊(C211⋊C8) | C2 | semidirect |
| 6. #27212876 | C2 | semidirect |
| 7. Q8⋊C8×C211 | C2 | semidirect |
| 30. Q8×D211 | C8 | semidirect |
| 103. C211 | #1479 | semidirect |
| 111. Q8⋊C8 | D211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×Q8×D211 | 2 |
| #27213198 | 2 |
| #27213197 | 2 |
| #27212878 | 2 |
| Q8⋊(C211⋊C8) | 2 |
| #27212876 | 2 |
| Q8⋊C8×C211 | 2 |
| #1479 | 211 |