Finite Group DatabasebetaFinite Group DatabasebetaOrder 14656.
108 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 108 conjugacy classes of subgroups — too many to draw. Only its 37 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. #20301013 | C2 | semidirect |
| 2. C2×#16814651 | C2 | semidirect |
| 3. #20300995 | C2 | semidirect |
| 4. #20300923 | C2 | semidirect |
| 5. #20300905 | C2 | semidirect |
| 6. #20300904 | C2 | semidirect |
| 7. AGL(1,ℤ/8)×C229 | C2 | semidirect |
| 53. C229 | #472 | semidirect |
| 56. AGL(1,ℤ/8) | D229 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20301013 | 2 |
| C2×#16814651 | 2 |
| #20300995 | 2 |
| #20300923 | 2 |
| #20300905 | 2 |
| #20300904 | 2 |
| AGL(1,ℤ/8)×C229 | 2 |
| #472 | 229 |