Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
340 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 340 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 |
|---|---|---|
| 3. #20299006 | C2 | semidirect |
| 4. #20299005 | C2 | semidirect |
| 5. #20298999 | C2 | semidirect |
| 6. #20298995 | C2 | semidirect |
| 44. C2×#11744751 | Q8 | semidirect |
| 65. M16×C113 | Q8 | semidirect |
| 113. C113 | #3163 | semidirect |
| 159. M16 | Dic226 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20299229 | 2 |
| #20299226 | 2 |
| #20299006 | 2 |
| #20299005 | 2 |
| #20298999 | 2 |
| #20298995 | 2 |
| #20298640 | 2 |
| #20298634 | 2 |
| C2×#16813553 | 2 |
| #20298556 | 2 |
| #428×C113 | 2 |
| #3163 | 113 |