Finite Group DatabasebetaFinite Group DatabasebetaOrder 14656.
124 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 53 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. C2×C8×D229 | C2 | semidirect |
| 3. #20300917 | C2 | semidirect |
| 4. C22⋊#14270080 | C2 | semidirect |
| 5. #20300900 | C2 | semidirect |
| 6. #20300898 | C2 | semidirect |
| 7. C2×M16×C229 | C2 | semidirect |
| 36. C8×C229 | D4 | semidirect |
| 43. C2×D229 | M16 | semidirect |
| 55. C229 | #435 | semidirect |
| 57. C2×M16 | D229 | semidirect |
| 92. C8 | C22⋊D229 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C8×D229 | 2 |
| C4×C22⋊D229 | 2 |
| #20300917 | 2 |
| C22⋊#14270080 | 2 |
| #20300900 | 2 |
| #20300898 | 2 |
| C2×M16×C229 | 2 |
| #435 | 229 |