Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
484 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 484 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. #20299155 | C2 | semidirect |
| 3. #20298963 | C2 | semidirect |
| 4. #20298945 | C2 | semidirect |
| 5. #20298604 | C2 | semidirect |
| 6. C4×M16×C113 | C2 | semidirect |
| 9. #16813622 | C22 | semidirect |
| 13. #16813614 | C22 | semidirect |
| 17. #16813544 | C22 | semidirect |
| 20. #97×C113 | C22 | semidirect |
| 21. C4×C8×C113 | C22 | semidirect |
| 75. C113 | #3138 | semidirect |
| 81. C4×M16 | D113 | semidirect |
| 95. #97 | C2×D113 | semidirect |
| 96. C4×C8 | C2×D113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20299155 | 2 |
| C2×#16813619 | 2 |
| #20298963 | 2 |
| #20298945 | 2 |
| #20298604 | 2 |
| C4×M16×C113 | 2 |
| #3138 | 113 |