Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
300 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 90 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. #20295989 | C2 | semidirect |
| 4. C2×C8×#89137 | C2 | semidirect |
| 5. #20295901 | C2 | semidirect |
| 6. #20295898 | C2 | semidirect |
| 12. #16812764 | C4 | semidirect |
| 13. #16812763 | C4 | semidirect |
| 14. #16812762 | C4 | semidirect |
| 15. #16812761 | C4 | semidirect |
| 22. #16812707 | C4 | semidirect |
| 23. #16812706 | C4 | semidirect |
| 25. #16812705 | C4 | semidirect |
| 30. #131×C109 | C4 | semidirect |
| 128. C109 | #1764 | semidirect |
| 142. #131 | #89137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D109⋊#104 | 2 |
| #20296016 | 2 |
| #20295989 | 2 |
| C2×C8×#89137 | 2 |
| #20295901 | 2 |
| #20295898 | 2 |
| #131×D109 | 2 |
| #1764 | 109 |