Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
256 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 57 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. #20298971 | C2 | semidirect |
| 3. #20298893 | C2 | semidirect |
| 4. #20298889 | C2 | semidirect |
| 5. #20298341 | C2 | semidirect |
| 6. #20298327 | C2 | semidirect |
| 7. Q8⋊C8×C113 | C2 | semidirect |
| 53. Q8×C113 | SD16 | semidirect |
| 99. C113 | #1631 | semidirect |
| 105. Q8⋊C8 | D113 | semidirect |
| 153. Q8 | #14268636 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20299270 | 2 |
| #20298971 | 2 |
| #20298893 | 2 |
| #20298889 | 2 |
| #20298341 | 2 |
| #20298327 | 2 |
| Q8⋊C8×C113 | 2 |
| #1631 | 113 |