Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
184 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 84 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) |
| 34. C2×C4×C97 | C16 | semidirect |
| 35. C2×Dic97 | C16 | semidirect |
| 36. C4×D97 | C16 | semidirect |
| 47. C4×C97 | C2×C16 | semidirect |
| 48. Dic97 | C2×C16 | semidirect |
| 49. C2×C97 | C4⋊C16 | semidirect |
| 51. D97 | C4⋊C16 | semidirect |
| 55. C97 | C2×C4⋊C16 | semidirect |
| 88. C2×C4 | #13095525 | semidirect |
| 103. C4 | C2×#13095525 | semidirect |
| 107. 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 |