Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
412 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 2. C2×#16813580 | C2 | semidirect |
| 3. C2×#16813544 | C2 | semidirect |
| 4. C2×#16813542 | C2 | semidirect |
| 5. C2×#16813534 | C2 | semidirect |
| 6. #20298360 | C2 | semidirect |
| 7. #340×C113 | C2 | semidirect |
| 13. #16813597 | C4 | semidirect |
| 49. C4⋊Dic113 | D4 | semidirect |
| 62. C4⋊C4×C113 | D4 | semidirect |
| 146. C113 | #1875 | semidirect |
| 153. #340 | D113 | semidirect |
| 205. C4⋊C4 | D452 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16813597 | 2 |
| C2×#16813580 | 2 |
| C2×#16813544 | 2 |
| C2×#16813542 | 2 |
| C2×#16813534 | 2 |
| #20298360 | 2 |
| #340×C113 | 2 |
| #1875 | 113 |