Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
1488 conjugacy classes of subgroups; only the 762 normal subgroups are shown.
This group has 1488 conjugacy classes of subgroups — too many to draw. Only its 762 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. #20299666 | C2 | direct (N × H) |
| 2. C2×Q8×#90673 | C2 | semidirect |
| 5. Q8×#90673 | C22 | semidirect |
| 10. C22×Dic226 | C4 | semidirect |
| 11. C2×Q8×D113 | C4 | semidirect |
| 12. C2×Q8×D113 | C4 | semidirect |
| 16. C22×Q8×C113 | C4 | semidirect |
| 23. C2×Dic226 | C2×C4 | semidirect |
| 25. Q8×D113 | C2×C4 | semidirect |
| 33. C2×Q8×C113 | C2×C4 | semidirect |
| 66. C2×C113 | #519 | semidirect |
| 69. D113 | #519 | semidirect |
| 72. C113 | C2×#519 | semidirect |
| 82. C22×Q8 | #90673 | semidirect |
| 96. C2×Q8 | C2×#90673 | semidirect |
| 141. C2 | #20299666 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20299666 | 2 |
| C2×Q8×#90673 | 2 |
| C2×#16813701 | 2 |
| C22×Q8×D113 | 2 |
| C2×#519 | 113 |