Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
224 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 224 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 |
|---|---|---|
| 9. #16812768 | C4 | semidirect |
| 10. #16812767 | C4 | semidirect |
| 12. #16812753 | C4 | semidirect |
| 13. #16812753 | C4 | semidirect |
| 17. #16812635 | C4 | semidirect |
| 18. #16812634 | C4 | semidirect |
| 19. #108×C109 | C4 | semidirect |
| 72. C109 | #1773 | semidirect |
| 85. #108 | #89137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20296036 | 2 |
| #20295992 | 2 |
| C2×#16812753 | 2 |
| #20295898 | 2 |
| #108×D109 | 2 |
| #1773 | 109 |