Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
160 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 53 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. #27213442 | C2 | semidirect |
| 4. C8×Dic422 | C2 | semidirect |
| 5. #27212894 | C2 | semidirect |
| 7. #334×C211 | C2 | semidirect |
| 76. C211 | #1678 | semidirect |
| 82. #334 | D211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27213493 | 2 |
| #27213442 | 2 |
| #27213347 | 2 |
| C8×Dic422 | 2 |
| #27212894 | 2 |
| #27212889 | 2 |
| #334×C211 | 2 |
| #1678 | 211 |