Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
216 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 116 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 |
|---|---|---|
| 2. C4×#13095525 | C2 | direct (N × H) |
| 4. C2×#13095525 | C4 | direct (N × H) |
| 11. #13095525 | C2×C4 | direct (N × H) |
| 23. C2×#87604 | C16 | semidirect |
| 32. C2×C4×C97 | C16 | semidirect |
| 33. C2×Dic97 | C16 | semidirect |
| 34. C4×D97 | C16 | semidirect |
| 42. #87604 | C2×C16 | semidirect |
| 45. C4×C97 | C2×C16 | semidirect |
| 46. Dic97 | C2×C16 | semidirect |
| 47. C2×C97 | C4×C16 | semidirect |
| 49. D97 | C4×C16 | semidirect |
| 53. C97 | C2×C4×C16 | semidirect |
| 85. C2×C4 | #13095525 | direct (N × H) |
| 99. C4 | C2×#13095525 | direct (N × H) |
| 103. C2 | C4×#13095525 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13095525 | 2 |
| C4×#13095525 | 2 |
| C2×C4×#11715906 | 2 |
| C2×C4×C16 | 97 |