Finite Group DatabasebetaFinite Group DatabasebetaOrder 14528.
270 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 103 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×Q8×D227 | C2 | semidirect |
| 3. #20300286 | C2 | semidirect |
| 4. #20300277 | C2 | semidirect |
| 5. #20300276 | C2 | semidirect |
| 6. #20300273 | C2 | semidirect |
| 7. #20300266 | C2 | semidirect |
| 8. #20300245 | C2 | semidirect |
| 9. C4⋊Q8×C227 | C2 | semidirect |
| 63. C227 | #536 | semidirect |
| 68. C4⋊Q8 | D227 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16813885 | 2 |
| C2×Q8×D227 | 2 |
| #20300286 | 2 |
| #20300277 | 2 |
| #20300276 | 2 |
| #20300273 | 2 |
| #20300266 | 2 |
| #20300245 | 2 |
| C4⋊Q8×C227 | 2 |
| #536 | 227 |