Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
430 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 119 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. #20299149 | C2 | semidirect |
| 2. C4×#14268648 | C2 | semidirect |
| 3. #20298924 | C2 | semidirect |
| 4. #20298875 | C2 | semidirect |
| 5. #20298798 | C2 | semidirect |
| 6. #20298794 | C2 | semidirect |
| 7. #20298746 | C2 | semidirect |
| 8. #20298709 | C2 | semidirect |
| 9. #20298701 | C2 | semidirect |
| 10. #20298654 | C2 | semidirect |
| 11. #475×C113 | C2 | semidirect |
| 88. Q8×C113 | #41 | semidirect |
| 106. D452 | #41 | semidirect |
| 145. C113 | #3115 | semidirect |
| 149. #475 | D113 | semidirect |
| 233. Q8 | #14268648 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20299149 | 2 |
| C4×#14268648 | 2 |
| #20298924 | 2 |
| #20298875 | 2 |
| #20298798 | 2 |
| #20298794 | 2 |
| #20298746 | 2 |
| #20298709 | 2 |
| #20298701 | 2 |
| #20298654 | 2 |
| #475×C113 | 2 |
| #3115 | 113 |