Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
172 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 172 conjugacy classes of subgroups — too many to draw. Only its 48 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. #20295953 | C2 | semidirect |
| 3. #20295938 | C2 | semidirect |
| 4. #20295913 | 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 |
| 54. C109 | #2177 | semidirect |
| 64. D16 | #89137 | semidirect |
| 74. D8 | C2×#89137 | semidirect |
| 82. 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 |
| #20295953 | 2 |
| #20295938 | 2 |
| #20295913 | 2 |
| D16×D109 | 2 |
| #2177 | 109 |