Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
232 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 85 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. #27212887 | C2 | direct (N × H) |
| 69. C2×C211 | #330 | semidirect |
| 73. C211 | C2×#330 | semidirect |
| 143. C2 | #27212887 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20269969 | 2 |
| C2×#20269888 | 2 |
| #27212887 | 2 |
| C2×#97×C211 | 2 |
| C2×#330 | 211 |