Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
398 conjugacy classes of subgroups; only the 166 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 166 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. #20299649 | C2 | semidirect |
| 2. #20299629 | C2 | semidirect |
| 3. D4×#11744753 | C2 | semidirect |
| 4. #20299618 | C2 | semidirect |
| 5. #20299615 | C2 | semidirect |
| 6. #20299601 | C2 | semidirect |
| 7. C2×#16813689 | C2 | semidirect |
| 64. D4×C113 | M16 | semidirect |
| 108. C113 | #2990 | semidirect |
| 172. D4 | #14268656 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20299649 | 2 |
| #20299629 | 2 |
| D4×#11744753 | 2 |
| #20299618 | 2 |
| #20299615 | 2 |
| #20299601 | 2 |
| C2×#16813689 | 2 |
| #41×Dic113 | 2 |
| #2990 | 113 |