Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
174 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 50 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 |
|---|---|---|
| 1. D8×#89137 | C2 | semidirect |
| 2. #20295952 | C2 | semidirect |
| 3. #20295938 | C2 | semidirect |
| 4. C16×#89137 | C2 | semidirect |
| 12. D1744 | C4 | semidirect |
| 13. #16812640 | C4 | semidirect |
| 15. D16×C109 | C4 | semidirect |
| 23. D872 | C2×C4 | semidirect |
| 26. #13182004 | C2×C4 | semidirect |
| 27. D8×C109 | C2×C4 | semidirect |
| 28. C16×C109 | C2×C4 | semidirect |
| 48. #89137 | D16 | direct (N × H) |
| 57. C109 | C4×D16 | semidirect |
| 67. D16 | #89137 | direct (N × H) |
| 77. D8 | C2×#89137 | semidirect |
| 85. C16 | C2×#89137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D8×#89137 | 2 |
| #20295952 | 2 |
| #20295938 | 2 |
| C16×#89137 | 2 |
| D16×D109 | 2 |
| C4×D16 | 109 |