Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
166 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 69 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. #27212896 | C2 | semidirect |
| 4. Q8⋊(C211⋊C8) | C2 | semidirect |
| 6. #27212867 | C2 | semidirect |
| 7. C8×Q8×C211 | C2 | semidirect |
| 52. Q8×C211 | M16 | semidirect |
| 60. C8×C211 | SD16 | semidirect |
| 77. C211 | #1583 | semidirect |
| 79. C8×Q8 | D211 | semidirect |
| 121. Q8 | #16809945 | semidirect |
| 138. C8 | #16809949 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#16809949 | 2 |
| #27213225 | 2 |
| #27212896 | 2 |
| Q8⋊(C211⋊C8) | 2 |
| #27212873 | 2 |
| #27212867 | 2 |
| C8×Q8×C211 | 2 |
| #1583 | 211 |