Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
256 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 117 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. #27212891 | C2 | direct (N × H) |
| 71. C2×C211 | #332 | semidirect |
| 75. C211 | C2×#332 | semidirect |
| 147. C2 | #27212891 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20269977 | 2 |
| C2×C4⋊(C211⋊C8) | 2 |
| #27212891 | 2 |
| C2×C4⋊C8×C211 | 2 |
| C2×#332 | 211 |