Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
166 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 65 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. Q8×#11744751 | C2 | semidirect |
| 4. #20298348 | C2 | semidirect |
| 6. #20298320 | C2 | semidirect |
| 7. Q8⋊C8×C113 | C2 | semidirect |
| 43. Q8×C113 | M16 | semidirect |
| 60. #11744751 | SD16 | semidirect |
| 78. C113 | #1583 | semidirect |
| 83. Q8⋊C8 | D113 | semidirect |
| 121. Q8 | #14268630 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×#11744751 | 2 |
| C4×#14268634 | 2 |
| #20298675 | 2 |
| #20298348 | 2 |
| #20298327 | 2 |
| #20298320 | 2 |
| Q8⋊C8×C113 | 2 |
| #1583 | 113 |