Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
656 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 656 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×#16813646 | C2 | semidirect |
| 2. #20299146 | C2 | semidirect |
| 3. #127×D113 | C2 | semidirect |
| 4. #20298986 | C2 | semidirect |
| 5. #20298974 | C2 | semidirect |
| 6. #20298971 | C2 | semidirect |
| 7. #20298970 | C2 | semidirect |
| 8. C4×#14268630 | C2 | semidirect |
| 9. #493×C113 | C2 | semidirect |
| 14. C2×#14268636 | C22 | semidirect |
| 15. C2×#14268635 | C22 | semidirect |
| 16. C2×#14268632 | C22 | semidirect |
| 18. #16813622 | C22 | semidirect |
| 22. #16813609 | C22 | semidirect |
| 26. #16813532 | C22 | semidirect |
| 27. C4×#11744751 | C22 | semidirect |
| 28. C2×D8×C113 | C22 | semidirect |
| 30. #127×C113 | C22 | semidirect |
| 31. C4×C8×C113 | C22 | semidirect |
| 48. #14268630 | D4 | semidirect |
| 85. C8×C113 | C2×D4 | semidirect |
| 86. #11744751 | C2×D4 | semidirect |
| 97. C4×C113 | AGL(1,ℤ/8) | semidirect |
| 109. C113 | #3151 | semidirect |
| 115. #493 | D113 | semidirect |
| 126. C2×D8 | C2×D113 | semidirect |
| 133. #127 | C2×D113 | semidirect |
| 140. C4×C8 | C2×D113 | semidirect |
| 195. C8 | D4×D113 | semidirect |
| 209. C4 | #16813646 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16813646 | 2 |
| #20299146 | 2 |
| #127×D113 | 2 |
| #20298986 | 2 |
| #20298974 | 2 |
| #20298971 | 2 |
| #20298970 | 2 |
| C4×#14268630 | 2 |
| #493×C113 | 2 |
| #3151 | 113 |