Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
196 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 12. #20269912 | C4 | semidirect |
| 84. C211 | #1951 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20269912 | 2 |
| #27213188 | 2 |
| #27213186 | 2 |
| C2×#20269908 | 2 |
| #27213104 | 2 |
| #27212914 | 2 |
| #343×C211 | 2 |
| #1951 | 211 |