Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
232 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 64 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. #20299654 | C2 | semidirect |
| 2. C2×#16813690 | C2 | semidirect |
| 3. #20299515 | C2 | semidirect |
| 4. #20299514 | C2 | semidirect |
| 7. #16813697 | C22 | semidirect |
| 11. #16813690 | C22 | semidirect |
| 14. #16813644 | C4 | semidirect |
| 18. Q16×D113 | C4 | semidirect |
| 20. D8×D113 | C4 | semidirect |
| 22. #135×C113 | C4 | semidirect |
| 37. Dic452 | C2×C4 | semidirect |
| 42. D904 | C2×C4 | semidirect |
| 50. Q16×C113 | C2×C4 | semidirect |
| 52. D8×C113 | C2×C4 | semidirect |
| 102. D113 | #360 | semidirect |
| 104. C113 | C2×#360 | semidirect |
| 116. #135 | #90673 | semidirect |
| 141. Q16 | C2×#90673 | semidirect |
| 148. D8 | C2×#90673 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20299654 | 2 |
| C2×#16813690 | 2 |
| #20299515 | 2 |
| #20299514 | 2 |
| #135×D113 | 2 |
| C2×#360 | 113 |