Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
512 conjugacy classes of subgroups; only the 218 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 218 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 |
|---|---|---|
| 3. #20299605 | C2 | direct (N × H) |
| 4. C2×#16813689 | C2 | semidirect |
| 5. C2×C4⋊#11744753 | C2 | semidirect |
| 14. #16813689 | C22 | semidirect |
| 15. C4⋊#11744753 | C22 | semidirect |
| 80. C2×C113 | #424 | semidirect |
| 86. C113 | C2×#424 | semidirect |
| 167. C2 | #20299605 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14268657 | 2 |
| C22×#14268655 | 2 |
| #20299605 | 2 |
| C2×#16813689 | 2 |
| C2×C4⋊#11744753 | 2 |
| C2×#16813580 | 2 |
| C2×#424 | 113 |