Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
180 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 180 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. #20298722 | C2 | semidirect |
| 4. #20298328 | C2 | semidirect |
| 6. C8×#11744751 | C2 | semidirect |
| 7. #334×C113 | C2 | semidirect |
| 26. #14268636 | C8 | semidirect |
| 53. Dic226 | C2×C8 | semidirect |
| 57. C8×C113 | C2×C8 | semidirect |
| 60. #11744751 | SD16 | semidirect |
| 78. C113 | C8×SD16 | semidirect |
| 82. #334 | D113 | semidirect |
| 138. C8 | C8×D113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20298722 | 2 |
| C4×#14268636 | 2 |
| #20298663 | 2 |
| #20298328 | 2 |
| #20298325 | 2 |
| C8×#11744751 | 2 |
| #334×C113 | 2 |
| C8×SD16 | 113 |