Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
356 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 139 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 |
|---|---|---|
| 2. #20299001 | C2 | semidirect |
| 3. #20298933 | C2 | semidirect |
| 4. #20298931 | C2 | semidirect |
| 5. #20298893 | C2 | semidirect |
| 6. #20298890 | C2 | semidirect |
| 7. #20298837 | C2 | semidirect |
| 8. C4×#14268637 | C2 | semidirect |
| 10. C2×#16813555 | C2 | semidirect |
| 77. D4×C113 | Q16 | semidirect |
| 118. C113 | #3338 | semidirect |
| 198. D4 | #14268637 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20299305 | 2 |
| #20299001 | 2 |
| #20298933 | 2 |
| #20298931 | 2 |
| #20298893 | 2 |
| #20298890 | 2 |
| #20298837 | 2 |
| C4×#14268637 | 2 |
| D4×#11744751 | 2 |
| C2×#16813555 | 2 |
| #554×C113 | 2 |
| #3338 | 113 |