Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
384 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 133 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. #20298908 | C2 | semidirect |
| 4. #20298904 | C2 | semidirect |
| 5. #20298901 | C2 | semidirect |
| 6. #20298897 | C2 | semidirect |
| 7. #20298641 | C2 | semidirect |
| 8. #20298621 | C2 | semidirect |
| 11. #428×C113 | C2 | semidirect |
| 136. C113 | #3080 | semidirect |
| 144. #428 | D113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16813613 | 2 |
| #20299066 | 2 |
| #20298908 | 2 |
| #20298904 | 2 |
| #20298901 | 2 |
| #20298897 | 2 |
| #20298641 | 2 |
| #20298621 | 2 |
| #20298600 | 2 |
| #20298597 | 2 |
| #428×C113 | 2 |
| #3080 | 113 |