Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
380 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 121 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. #20299135 | C2 | semidirect |
| 2. #20298999 | C2 | semidirect |
| 3. #20298983 | C2 | semidirect |
| 4. #20298954 | C2 | semidirect |
| 5. #20298836 | C2 | semidirect |
| 7. #20298830 | C2 | semidirect |
| 8. C4×#14268634 | C2 | semidirect |
| 9. C4×D904 | C2 | semidirect |
| 10. C4×C8×D113 | C2 | semidirect |
| 11. C4×Q16×C113 | C2 | semidirect |
| 119. C113 | #3168 | semidirect |
| 127. C4×Q16 | D113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20299135 | 2 |
| #20298999 | 2 |
| #20298983 | 2 |
| #20298954 | 2 |
| #20298836 | 2 |
| #20298835 | 2 |
| #20298830 | 2 |
| C4×#14268634 | 2 |
| C4×D904 | 2 |
| C4×C8×D113 | 2 |
| C4×Q16×C113 | 2 |
| #3168 | 113 |