Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
500 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 500 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×#16812730 | C2 | semidirect |
| 3. C2×#16812688 | C2 | semidirect |
| 4. #20295494 | C2 | semidirect |
| 5. #20295251 | C2 | semidirect |
| 6. #20295244 | C2 | semidirect |
| 7. #20295049 | C2 | semidirect |
| 8. #20295030 | C2 | semidirect |
| 9. #419×C109 | C2 | semidirect |
| 14. C2×#13182019 | C22 | semidirect |
| 16. C2×#13182016 | C22 | semidirect |
| 22. #16812664 | C22 | semidirect |
| 23. #16812661 | C22 | semidirect |
| 29. #16812628 | C22 | semidirect |
| 34. #103×C109 | C22 | semidirect |
| 126. C109 | #3040 | semidirect |
| 134. #419 | D109 | semidirect |
| 159. #103 | C2×D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812730 | 2 |
| C2×#16812727 | 2 |
| C2×#16812688 | 2 |
| #20295494 | 2 |
| #20295251 | 2 |
| #20295244 | 2 |
| #20295049 | 2 |
| #20295030 | 2 |
| #419×C109 | 2 |
| #3040 | 109 |