Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
190 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 190 conjugacy classes of subgroups — too many to draw. Only its 59 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. #27212918 | C2 | semidirect |
| 5. #27212911 | C2 | semidirect |
| 6. #27212902 | C2 | semidirect |
| 7. #424×C211 | C2 | semidirect |
| 89. C211 | #2080 | semidirect |
| 91. #424 | D211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27213164 | 2 |
| #27213143 | 2 |
| #27213128 | 2 |
| #27212918 | 2 |
| #27212911 | 2 |
| #27212902 | 2 |
| #424×C211 | 2 |
| #2080 | 211 |