Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
698 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 698 conjugacy classes of subgroups — too many to draw. Only its 145 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. C2×#16813669 | C2 | semidirect |
| 2. #20299396 | C2 | semidirect |
| 3. #20299169 | C2 | semidirect |
| 4. #20298779 | C2 | semidirect |
| 5. #20298769 | C2 | semidirect |
| 6. #20298615 | C2 | semidirect |
| 7. #20298614 | C2 | semidirect |
| 8. C2×#16813540 | C2 | semidirect |
| 9. #575×C113 | C2 | semidirect |
| 21. #16813653 | C22 | semidirect |
| 23. #16813648 | C22 | semidirect |
| 27. #16813620 | C22 | semidirect |
| 28. #16813609 | C22 | semidirect |
| 32. #16813549 | C22 | semidirect |
| 33. #16813548 | C22 | semidirect |
| 34. #16813540 | C22 | semidirect |
| 38. #137×C113 | C22 | semidirect |
| 40. AGL(1,ℤ/8)×C113 | C22 | semidirect |
| 186. C113 | #3020 | semidirect |
| 189. #575 | D113 | semidirect |
| 212. #137 | C2×D113 | semidirect |
| 216. AGL(1,ℤ/8) | C2×D113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16813669 | 2 |
| #20299396 | 2 |
| #20299169 | 2 |
| #20298779 | 2 |
| #20298769 | 2 |
| #20298615 | 2 |
| #20298614 | 2 |
| C2×#16813540 | 2 |
| #575×C113 | 2 |
| #3020 | 113 |