Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
348 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 149 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. #20299006 | C2 | semidirect |
| 3. #20299005 | C2 | semidirect |
| 27. C2×#11744751 | Q8 | semidirect |
| 38. C2×C8×C113 | Q8 | semidirect |
| 70. C113 | #3162 | semidirect |
| 100. C2×C8 | Dic226 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20299151 | 2 |
| #20299006 | 2 |
| #20299005 | 2 |
| #20298636 | 2 |
| #20298634 | 2 |
| C2×#16813532 | 2 |
| #427×C113 | 2 |
| #3162 | 113 |