Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
166 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 166 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 |
|---|---|---|
| 1. Q8×C211⋊C8 | C2 | semidirect |
| 3. #27212897 | C2 | semidirect |
| 4. Q8⋊(C211⋊C8) | C2 | semidirect |
| 6. #27212868 | C2 | semidirect |
| 45. C211⋊C8 | SD16 | semidirect |
| 48. Q8×C211 | M16 | semidirect |
| 77. C211 | #1583 | semidirect |
| 121. Q8 | #16809946 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×C211⋊C8 | 2 |
| #27213224 | 2 |
| #27212897 | 2 |
| Q8⋊(C211⋊C8) | 2 |
| D4⋊(C211⋊C8) | 2 |
| #27212868 | 2 |
| C4×SD16×C211 | 2 |
| #1583 | 211 |