Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
460 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 127 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×Q16×D113 | C2 | semidirect |
| 4. #20298855 | C2 | semidirect |
| 5. #20298854 | C2 | semidirect |
| 6. #20298840 | C2 | semidirect |
| 7. #20298839 | C2 | semidirect |
| 8. #20298836 | C2 | semidirect |
| 9. #20298635 | C2 | semidirect |
| 10. #20298605 | C2 | semidirect |
| 11. #467×C113 | C2 | semidirect |
| 138. C113 | #3059 | semidirect |
| 147. #467 | D113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×D113 | 2 |
| C2×#16813628 | 2 |
| #20299171 | 2 |
| #20298855 | 2 |
| #20298854 | 2 |
| #20298840 | 2 |
| #20298839 | 2 |
| #20298836 | 2 |
| #20298635 | 2 |
| #20298605 | 2 |
| #467×C113 | 2 |
| #3059 | 113 |