Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
420 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 420 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. #20299249 | C2 | semidirect |
| 2. #20299002 | C2 | semidirect |
| 3. #20298913 | C2 | semidirect |
| 4. #20298911 | C2 | semidirect |
| 5. #20298877 | C2 | semidirect |
| 6. #20298835 | C2 | semidirect |
| 7. #20298834 | C2 | semidirect |
| 8. #20298680 | C2 | semidirect |
| 9. C8×C22⋊D113 | C2 | semidirect |
| 10. #107×D113 | C2 | semidirect |
| 11. C2×#107×C113 | C2 | semidirect |
| 81. C22⋊D113 | D8 | semidirect |
| 95. C8×C113 | #41 | semidirect |
| 124. C113 | #3334 | semidirect |
| 135. C2×#107 | D113 | semidirect |
| 221. C8 | #14268647 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20299249 | 2 |
| #20299002 | 2 |
| #20298913 | 2 |
| #20298911 | 2 |
| #20298877 | 2 |
| #20298835 | 2 |
| #20298834 | 2 |
| #20298680 | 2 |
| C8×C22⋊D113 | 2 |
| #107×D113 | 2 |
| C2×#107×C113 | 2 |
| #3334 | 113 |