Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
312 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 78 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. #20299603 | C2 | semidirect |
| 3. C4×C4⋊#90673 | C2 | semidirect |
| 4. #20299468 | C2 | semidirect |
| 14. C4×Dic226 | C4 | semidirect |
| 15. #16813587 | C4 | semidirect |
| 16. D4×Dic113 | C4 | semidirect |
| 23. C4×D4×C113 | C4 | semidirect |
| 64. D4×C113 | C4⋊C4 | semidirect |
| 87. Dic226 | C4⋊C4 | semidirect |
| 106. Dic113 | #104 | semidirect |
| 116. C113 | #1806 | semidirect |
| 129. C4×D4 | #90673 | semidirect |
| 181. D4 | C4⋊#90673 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20299603 | 2 |
| C2×#16813686 | 2 |
| C4×C4⋊#90673 | 2 |
| #20299468 | 2 |
| C4×#14268646 | 2 |
| #1806 | 113 |