Finite Group DatabasebetaFinite Group DatabasebetaOrder 14656.
152 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 43 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. C2×#16814656 | C2 | semidirect |
| 3. C2×#16814653 | C2 | semidirect |
| 4. #20300911 | C2 | semidirect |
| 5. #20300908 | C2 | semidirect |
| 6. C22⋊#14270080 | C2 | semidirect |
| 7. C22⋊Q8×C229 | C2 | semidirect |
| 60. C229 | #452 | semidirect |
| 65. C22⋊Q8 | D229 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16814666 | 2 |
| C2×#16814656 | 2 |
| C2×#16814653 | 2 |
| #20300911 | 2 |
| #20300908 | 2 |
| C22⋊#14270080 | 2 |
| C22⋊Q8×C229 | 2 |
| #452 | 229 |