Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
398 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 398 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 |
|---|---|---|
| 2. #20299079 | C2 | semidirect |
| 3. #20298941 | C2 | semidirect |
| 4. #20298935 | C2 | semidirect |
| 5. #20298925 | C2 | semidirect |
| 6. #20298913 | C2 | semidirect |
| 7. #20298638 | C2 | semidirect |
| 8. #20298597 | C2 | semidirect |
| 9. #20298595 | C2 | semidirect |
| 10. #20298564 | C2 | semidirect |
| 11. C2×#107×C113 | C2 | semidirect |
| 134. C113 | #3098 | semidirect |
| 142. C2×#107 | D113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20299179 | 2 |
| #20299079 | 2 |
| #20298941 | 2 |
| #20298935 | 2 |
| #20298925 | 2 |
| #20298913 | 2 |
| #20298638 | 2 |
| #20298597 | 2 |
| #20298595 | 2 |
| #20298564 | 2 |
| C2×#107×C113 | 2 |
| #3098 | 113 |