Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
266 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 266 conjugacy classes of subgroups — too many to draw. Only its 73 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. #20298620 | C2 | semidirect |
| 3. C4×#14268630 | C2 | semidirect |
| 4. Q8⋊#11744751 | C2 | semidirect |
| 5. #20298327 | C2 | semidirect |
| 6. #20298325 | C2 | semidirect |
| 7. Q8⋊C8×C113 | C2 | semidirect |
| 61. Q8×C113 | M16 | semidirect |
| 73. D452 | M16 | semidirect |
| 111. C113 | #1489 | semidirect |
| 116. Q8⋊C8 | D113 | semidirect |
| 172. Q8 | #14268630 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14268648 | 2 |
| #20298620 | 2 |
| C4×#14268630 | 2 |
| Q8⋊#11744751 | 2 |
| #20298327 | 2 |
| #20298325 | 2 |
| Q8⋊C8×C113 | 2 |
| #1489 | 113 |