Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
452 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 137 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. #20299396 | C2 | semidirect |
| 2. C2×#16813628 | C2 | semidirect |
| 3. #20298870 | C2 | semidirect |
| 4. #20298865 | C2 | semidirect |
| 5. #20298858 | C2 | semidirect |
| 6. C2×#16813558 | C2 | semidirect |
| 7. #20298582 | C2 | semidirect |
| 8. C2×#135×C113 | C2 | semidirect |
| 23. #16813558 | C22 | semidirect |
| 24. #16813558 | C22 | semidirect |
| 25. #16813541 | C22 | semidirect |
| 26. #16813539 | C22 | semidirect |
| 32. C2×Q16×C113 | C22 | semidirect |
| 33. C2×SD16×C113 | C22 | semidirect |
| 34. C2×D8×C113 | C22 | semidirect |
| 133. C113 | #3067 | semidirect |
| 135. C2×#135 | D113 | semidirect |
| 153. C2×Q16 | C2×D113 | semidirect |
| 154. C2×SD16 | C2×D113 | semidirect |
| 155. C2×D8 | C2×D113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20299396 | 2 |
| C2×#16813628 | 2 |
| #20298870 | 2 |
| #20298865 | 2 |
| #20298858 | 2 |
| C2×#16813558 | 2 |
| #20298582 | 2 |
| C2×#135×C113 | 2 |
| #3067 | 113 |