Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
168 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 80 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. #20295917 | C2 | semidirect |
| 4. #20295916 | C2 | semidirect |
| 9. #16812773 | C4 | semidirect |
| 10. D109⋊C16 | C4 | semidirect |
| 16. #16812639 | C4 | semidirect |
| 18. C16×D109 | C4 | semidirect |
| 19. M32×C109 | C4 | semidirect |
| 28. #13182032 | C2×C4 | semidirect |
| 35. #13182004 | C2×C4 | semidirect |
| 37. C16×C109 | C2×C4 | semidirect |
| 67. D109 | #347 | semidirect |
| 69. C109 | C2×#347 | semidirect |
| 82. M32 | #89137 | semidirect |
| 106. C16 | C2×#89137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D109⋊M32 | 2 |
| C2×#16812753 | 2 |
| #20295917 | 2 |
| #20295916 | 2 |
| M32×D109 | 2 |
| C2×#347 | 109 |