Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
448 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 157 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×#16813613 | C2 | semidirect |
| 3. #20298896 | C2 | direct (N × H) |
| 4. C2×#16813556 | C2 | semidirect |
| 5. C2×#16813553 | C2 | semidirect |
| 6. C2×#16813551 | C2 | semidirect |
| 12. #16813613 | C22 | semidirect |
| 21. #16813556 | C22 | semidirect |
| 22. #16813553 | C22 | semidirect |
| 23. #16813551 | C22 | semidirect |
| 99. C2×C113 | #478 | semidirect |
| 104. C113 | C2×#478 | semidirect |
| 203. C2 | #20298896 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16813613 | 2 |
| C2×D4×Dic113 | 2 |
| #20298896 | 2 |
| C2×#16813556 | 2 |
| C2×#16813553 | 2 |
| C2×#16813551 | 2 |
| C2×#16813543 | 2 |
| C2×#102×C113 | 2 |
| C2×#478 | 113 |