Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
196 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 73 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. #27213211 | C2 | semidirect |
| 3. #27212873 | C2 | semidirect |
| 4. C8×C211⋊C8 | C2 | semidirect |
| 5. #335×C211 | C2 | semidirect |
| 18. D1688 | C8 | semidirect |
| 31. D844 | C2×C8 | semidirect |
| 37. C211⋊C8 | D8 | semidirect |
| 43. C8×C211 | C2×C8 | semidirect |
| 58. C211 | C8×D8 | semidirect |
| 62. #335 | D211 | semidirect |
| 102. C8 | C8×D211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D1688 | 2 |
| #27213211 | 2 |
| #27212873 | 2 |
| C8×C211⋊C8 | 2 |
| #335×C211 | 2 |
| C8×D8 | 211 |