Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
392 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 141 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. #20298946 | C2 | semidirect |
| 3. #20298885 | C2 | semidirect |
| 4. #20298798 | C2 | semidirect |
| 5. Q8×#11744751 | C2 | semidirect |
| 6. C4×#14268634 | C2 | semidirect |
| 7. Q82×C113 | C2 | semidirect |
| 46. Q8×C113 | SD16 | semidirect |
| 47. Q8×C113 | #41 | semidirect |
| 77. C113 | #3362 | semidirect |
| 78. Q82 | D113 | semidirect |
| 123. Q8 | #14268634 | semidirect |
| 124. Q8 | #14268648 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20299270 | 2 |
| #20298946 | 2 |
| #20298885 | 2 |
| #20298798 | 2 |
| Q8×#11744751 | 2 |
| C4×#14268634 | 2 |
| Q82×C113 | 2 |
| #3362 | 113 |