Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
500 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 141 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×#16812732 | C2 | semidirect |
| 3. C2×#16812687 | C2 | semidirect |
| 4. C4×#13182029 | C2 | semidirect |
| 5. #20295249 | C2 | semidirect |
| 6. #20295242 | C2 | semidirect |
| 7. #20295036 | C2 | semidirect |
| 8. #20295032 | C2 | semidirect |
| 9. #423×C109 | C2 | semidirect |
| 15. C2×Dic436 | C22 | semidirect |
| 17. C2×#13182018 | C22 | semidirect |
| 22. C4×Dic218 | C22 | semidirect |
| 23. C4×D436 | C22 | semidirect |
| 29. #16812624 | C22 | semidirect |
| 34. C4⋊C8×C109 | C22 | semidirect |
| 126. C109 | #3040 | semidirect |
| 133. #423 | D109 | semidirect |
| 158. C4⋊C8 | C2×D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812732 | 2 |
| C2×#16812727 | 2 |
| C2×#16812687 | 2 |
| C4×#13182029 | 2 |
| #20295249 | 2 |
| #20295242 | 2 |
| #20295036 | 2 |
| #20295032 | 2 |
| #423×C109 | 2 |
| #3040 | 109 |