Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
216 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 122 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. C16×#89137 | C2 | direct (N × H) |
| 7. D109⋊C16 | C4 | semidirect |
| 9. C2×#13182032 | C4 | semidirect |
| 13. C2×#13182004 | C4 | semidirect |
| 14. C16×D109 | C4 | semidirect |
| 16. C2×C16×C109 | C4 | semidirect |
| 23. #13182032 | C2×C4 | semidirect |
| 30. #13182004 | C2×C4 | semidirect |
| 32. C16×C109 | C2×C4 | semidirect |
| 34. C2×#89137 | C16 | direct (N × H) |
| 51. #89137 | C2×C16 | direct (N × H) |
| 56. C2×C109 | C4×C16 | semidirect |
| 58. D109 | C4×C16 | semidirect |
| 61. C109 | C2×C4×C16 | semidirect |
| 75. C2×C16 | #89137 | direct (N × H) |
| 93. C16 | C2×#89137 | direct (N × H) |
| 119. C2 | C16×#89137 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D109⋊C16 | 2 |
| C2×C8×#89137 | 2 |
| C16×#89137 | 2 |
| C2×C16×D109 | 2 |
| C2×C4×C16 | 109 |