Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
548 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 131 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. C4×D4×D113 | C2 | semidirect |
| 4. #20298812 | C2 | semidirect |
| 5. #20298811 | C2 | semidirect |
| 6. #20298804 | C2 | semidirect |
| 7. #20298803 | C2 | semidirect |
| 8. #20298790 | C2 | semidirect |
| 9. #20298620 | C2 | semidirect |
| 10. #20298596 | C2 | semidirect |
| 11. #459×C113 | C2 | semidirect |
| 20. #16813622 | C22 | semidirect |
| 21. #16813609 | C22 | semidirect |
| 34. C4⋊#11744751 | C22 | semidirect |
| 35. #16813551 | C22 | semidirect |
| 36. #16813547 | C22 | semidirect |
| 37. #16813545 | C22 | semidirect |
| 38. #16813543 | C22 | semidirect |
| 40. #127×C113 | C22 | semidirect |
| 42. C4⋊C8×C113 | C22 | semidirect |
| 43. #102×C113 | C22 | semidirect |
| 52. D4×D113 | D4 | semidirect |
| 145. C4×C113 | AGL(1,ℤ/8) | semidirect |
| 161. C113 | #3036 | semidirect |
| 170. #459 | D113 | semidirect |
| 183. #127 | C2×D113 | semidirect |
| 200. C4⋊C8 | C2×D113 | semidirect |
| 204. #102 | C2×D113 | semidirect |
| 311. 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 |
| C4×D4×D113 | 2 |
| #20298812 | 2 |
| #20298811 | 2 |
| #20298804 | 2 |
| #20298803 | 2 |
| #20298790 | 2 |
| #20298620 | 2 |
| #20298596 | 2 |
| #459×C113 | 2 |
| #3036 | 113 |