Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
466 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 466 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 |
|---|---|---|
| 2. #27212913 | C2 | semidirect |
| 3. #543×C211 | C2 | semidirect |
| 12. C23×D211 | Q8 | semidirect |
| 55. C211 | #2029 | semidirect |
| 57. #543 | D211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27213001 | 2 |
| #27212913 | 2 |
| #543×C211 | 2 |
| #2029 | 211 |