Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
300 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 88 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 |
|---|---|---|
| 3. #20295992 | C2 | semidirect |
| 4. C4×D109⋊C8 | C2 | semidirect |
| 5. #20295901 | C2 | semidirect |
| 6. #20295897 | C2 | semidirect |
| 8. #16812787 | C4 | semidirect |
| 10. #16812786 | C4 | semidirect |
| 17. #16812762 | C4 | semidirect |
| 18. #16812761 | C4 | semidirect |
| 25. #16812627 | C4 | semidirect |
| 26. #16812626 | C4 | semidirect |
| 27. #16812625 | C4 | semidirect |
| 28. #104×C109 | C4 | semidirect |
| 121. C109 | #1764 | semidirect |
| 144. #104 | #89137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D109⋊#131 | 2 |
| #20296016 | 2 |
| #20295992 | 2 |
| C4×D109⋊C8 | 2 |
| #20295901 | 2 |
| #20295897 | 2 |
| #104×D109 | 2 |
| #1764 | 109 |