Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
456 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 79 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×C22⋊#11744762 | C2 | semidirect |
| 2. #20299683 | C2 | direct (N × H) |
| 6. C22⋊#11744762 | C22 | semidirect |
| 33. C23×D113 | C8 | semidirect |
| 34. C23×D113 | C8 | semidirect |
| 37. C24×C113 | C8 | semidirect |
| 42. C23×C113 | C2×C8 | semidirect |
| 64. C22×D113 | C2×C8 | semidirect |
| 115. C2×C113 | #323 | semidirect |
| 120. D113 | #323 | semidirect |
| 124. C113 | C2×#323 | semidirect |
| 148. C24 | #11744762 | semidirect |
| 191. C23 | C2×#11744762 | semidirect |
| 245. C2 | #20299683 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C22⋊#11744762 | 2 |
| #20299683 | 2 |
| C22×C22⋊#90673 | 2 |
| C2×#323 | 113 |