Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
448 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 448 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 |
|---|---|---|
| 3. #20298870 | C2 | direct (N × H) |
| 4. C2×#16813558 | C2 | semidirect |
| 5. C2×#16813541 | C2 | semidirect |
| 6. C22×Q16×C113 | C2 | semidirect |
| 18. #16813558 | C22 | semidirect |
| 19. #16813541 | C22 | semidirect |
| 24. C2×Q16×C113 | C22 | semidirect |
| 100. C2×C113 | #473 | semidirect |
| 104. C113 | C2×#473 | semidirect |
| 106. C22×Q16 | D113 | semidirect |
| 119. C2×Q16 | C2×D113 | semidirect |
| 205. C2 | #20298870 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16813653 | 2 |
| C2×#16813628 | 2 |
| #20298870 | 2 |
| C2×#16813558 | 2 |
| C2×#16813541 | 2 |
| C22×Q16×C113 | 2 |
| C2×#473 | 113 |