Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
256 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 2. #27213199 | C2 | semidirect |
| 3. #27212893 | C2 | semidirect |
| 4. #27212889 | C2 | semidirect |
| 5. C2×C4⋊C8×C211 | C2 | semidirect |
| 86. C211 | #1540 | semidirect |
| 90. C2×C4⋊C8 | D211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27213696 | 2 |
| #27213199 | 2 |
| #27212893 | 2 |
| #27212889 | 2 |
| C2×C4⋊C8×C211 | 2 |
| #1540 | 211 |