Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
160 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 57 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 |
|---|---|---|
| 3. #27212899 | C2 | semidirect |
| 4. #27212895 | C2 | semidirect |
| 5. #500×C211 | C2 | semidirect |
| 60. C211 | #1675 | semidirect |
| 62. #500 | D211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27213433 | 2 |
| C8×D844 | 2 |
| #27212899 | 2 |
| #27212895 | 2 |
| #500×C211 | 2 |
| #1675 | 211 |