Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
384 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 125 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. #20299333 | C2 | semidirect |
| 2. #20298960 | C2 | semidirect |
| 3. #20298946 | C2 | semidirect |
| 4. #20298885 | C2 | semidirect |
| 5. #20298880 | C2 | semidirect |
| 6. #20298813 | C2 | semidirect |
| 8. #20298729 | C2 | semidirect |
| 9. #20298708 | C2 | semidirect |
| 10. C4×#14268635 | C2 | semidirect |
| 11. D4×Q8×C113 | C2 | semidirect |
| 125. C113 | #3373 | semidirect |
| 127. D4×Q8 | D113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20299333 | 2 |
| #20298960 | 2 |
| #20298946 | 2 |
| #20298885 | 2 |
| #20298880 | 2 |
| #20298813 | 2 |
| #20298793 | 2 |
| #20298729 | 2 |
| #20298708 | 2 |
| C4×#14268635 | 2 |
| D4×Q8×C113 | 2 |
| #3373 | 113 |