Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
232 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 75 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. #27213102 | C2 | semidirect |
| 5. #27212915 | C2 | semidirect |
| 6. #27212910 | C2 | semidirect |
| 7. #428×C211 | C2 | semidirect |
| 16. #20269893 | C4 | semidirect |
| 100. C211 | #1931 | semidirect |
| 102. #428 | D211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27213150 | 2 |
| C2×#20269897 | 2 |
| C2×#20269893 | 2 |
| #27213102 | 2 |
| #27212915 | 2 |
| #27212910 | 2 |
| #428×C211 | 2 |
| #1931 | 211 |