Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
444 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 125 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. #20299413 | C2 | semidirect |
| 2. #20299412 | C2 | semidirect |
| 3. #20298976 | C2 | semidirect |
| 4. #20298873 | C2 | semidirect |
| 5. #20298871 | C2 | semidirect |
| 6. #20298870 | C2 | semidirect |
| 7. #20298781 | C2 | semidirect |
| 8. #20298779 | C2 | semidirect |
| 9. #20298715 | C2 | semidirect |
| 10. #20298713 | C2 | semidirect |
| 11. #578×C113 | C2 | semidirect |
| 147. C113 | #3293 | semidirect |
| 150. #578 | D113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20299413 | 2 |
| #20299412 | 2 |
| #20298976 | 2 |
| #20298873 | 2 |
| #20298871 | 2 |
| #20298870 | 2 |
| #20298781 | 2 |
| #20298779 | 2 |
| #20298715 | 2 |
| #20298713 | 2 |
| #578×C113 | 2 |
| #3293 | 113 |