Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
394 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 121 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. #20299210 | C2 | semidirect |
| 3. #20298940 | C2 | semidirect |
| 4. #20298899 | C2 | semidirect |
| 5. #20298804 | C2 | semidirect |
| 7. #20298700 | C2 | semidirect |
| 8. C4×#14268636 | C2 | semidirect |
| 9. #433×C113 | C2 | semidirect |
| 13. #16813622 | C22 | semidirect |
| 15. #16813614 | C22 | semidirect |
| 18. C4×Dic226 | C22 | semidirect |
| 24. #16813556 | C22 | semidirect |
| 25. #16813554 | C22 | semidirect |
| 26. #16813547 | C22 | semidirect |
| 27. #16813547 | C22 | semidirect |
| 31. C4⋊C8×C113 | C22 | semidirect |
| 33. #97×C113 | C22 | semidirect |
| 34. C4×C8×C113 | C22 | semidirect |
| 103. C113 | #3123 | semidirect |
| 112. #433 | D113 | semidirect |
| 130. C4⋊C8 | C2×D113 | semidirect |
| 136. #97 | C2×D113 | semidirect |
| 137. C4×C8 | C2×D113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20299210 | 2 |
| #20299072 | 2 |
| #20298940 | 2 |
| #20298899 | 2 |
| #20298804 | 2 |
| #20298751 | 2 |
| #20298700 | 2 |
| C4×#14268636 | 2 |
| #433×C113 | 2 |
| #3123 | 113 |