Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
336 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 72 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×#16813687 | C2 | semidirect |
| 2. C2×#16813686 | C2 | semidirect |
| 3. C4×#14268657 | C2 | semidirect |
| 4. C4×C4⋊#90673 | C2 | semidirect |
| 16. #16813620 | C4 | semidirect |
| 17. #16813618 | C4 | semidirect |
| 18. #16813610 | C4 | semidirect |
| 24. #124×C113 | C4 | semidirect |
| 27. #14268657 | D4 | semidirect |
| 108. Dic113 | #104 | semidirect |
| 118. C113 | #1980 | semidirect |
| 130. #124 | #90673 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16813687 | 2 |
| C2×#16813686 | 2 |
| C4×#14268657 | 2 |
| C4×C4⋊#90673 | 2 |
| #20299147 | 2 |
| #1980 | 113 |