Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
456 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 129 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. #20299145 | C2 | semidirect |
| 2. #20299002 | C2 | semidirect |
| 3. #20298973 | C2 | semidirect |
| 4. #20298943 | C2 | semidirect |
| 5. #20298835 | C2 | semidirect |
| 6. #20298833 | C2 | semidirect |
| 7. #20298831 | C2 | semidirect |
| 8. C4×D904 | C2 | semidirect |
| 9. C4×#14268632 | C2 | semidirect |
| 10. C4×C8×D113 | C2 | semidirect |
| 11. C4×D8×C113 | C2 | semidirect |
| 96. C4×D113 | D8 | semidirect |
| 99. C8×C113 | #41 | semidirect |
| 101. #11744751 | #41 | semidirect |
| 128. C113 | #3169 | semidirect |
| 138. C4×D8 | D113 | semidirect |
| 229. C8 | #14268647 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20299145 | 2 |
| #20299002 | 2 |
| #20298973 | 2 |
| #20298943 | 2 |
| #20298835 | 2 |
| #20298833 | 2 |
| #20298831 | 2 |
| C4×D904 | 2 |
| C4×#14268632 | 2 |
| C4×C8×D113 | 2 |
| C4×D8×C113 | 2 |
| #3169 | 113 |