Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
398 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 141 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. #20299226 | C2 | semidirect |
| 3. #20298899 | C2 | semidirect |
| 4. #20298899 | C2 | semidirect |
| 5. #20298889 | C2 | semidirect |
| 6. #20298879 | C2 | semidirect |
| 7. #20298640 | C2 | semidirect |
| 8. #20298636 | C2 | semidirect |
| 11. #424×C113 | C2 | semidirect |
| 13. #16813622 | C22 | semidirect |
| 15. #16813614 | C22 | semidirect |
| 26. #16813556 | C22 | semidirect |
| 27. #16813556 | C22 | semidirect |
| 28. #16813556 | C22 | semidirect |
| 29. #16813554 | C22 | semidirect |
| 30. #16813554 | C22 | semidirect |
| 31. #16813554 | C22 | semidirect |
| 39. C4⋊C8×C113 | C22 | semidirect |
| 40. C4⋊C8×C113 | C22 | semidirect |
| 45. C2×D452 | Q8 | semidirect |
| 125. C113 | #3081 | semidirect |
| 134. #424 | D113 | semidirect |
| 160. C4⋊C8 | C2×D113 | semidirect |
| 161. C4⋊C8 | C2×D113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20299226 | 2 |
| #20299072 | 2 |
| #20298899 | 2 |
| #20298889 | 2 |
| #20298879 | 2 |
| #20298640 | 2 |
| #20298636 | 2 |
| #20298604 | 2 |
| C2×#16813544 | 2 |
| #424×C113 | 2 |
| #3081 | 113 |