Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
360 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 121 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. C42×Dic109 | C2 | semidirect |
| 4. #20294787 | C2 | semidirect |
| 5. C4×M16×C109 | C2 | semidirect |
| 7. C4×Dic218 | C4 | semidirect |
| 8. C4×D436 | C4 | semidirect |
| 15. #16812625 | C4 | direct (N × H) |
| 36. C4×Dic109 | C2×C4 | semidirect |
| 40. M16×C109 | C2×C4 | semidirect |
| 60. D436 | C42 | semidirect |
| 64. Dic218 | C42 | semidirect |
| 72. C4×C109 | #104 | semidirect |
| 84. C109 | C4×#104 | semidirect |
| 87. C4×M16 | D109 | semidirect |
| 115. M16 | C4×D109 | semidirect |
| 159. C4 | #16812625 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#13182029 | 2 |
| C2×#16812625 | 2 |
| C42×Dic109 | 2 |
| #20294787 | 2 |
| C4×M16×C109 | 2 |
| C4×#104 | 109 |