Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
210 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 210 conjugacy classes of subgroups — too many to draw. Only its 55 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. #27213874 | C2 | semidirect |
| 5. #27212891 | C2 | semidirect |
| 6. #27212878 | C2 | semidirect |
| 7. Q8⋊C8×C211 | C2 | semidirect |
| 53. Dic422 | SD16 | semidirect |
| 90. C211 | #1626 | semidirect |
| 98. Q8⋊C8 | D211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27213874 | 2 |
| #27213493 | 2 |
| #27213347 | 2 |
| #27213346 | 2 |
| #27212891 | 2 |
| #27212878 | 2 |
| Q8⋊C8×C211 | 2 |
| #1626 | 211 |