Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
174 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 64 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. C22×#13095525 | C2 | semidirect |
| 2. C4⋊#13095525 | C2 | semidirect |
| 3. C22⋊#13095525 | C2 | semidirect |
| 4. C4×#13095525 | C2 | semidirect |
| 17. #13095525 | D4 | direct (N × H) |
| 38. D4×C97 | C16 | semidirect |
| 39. C22⋊D97 | C16 | semidirect |
| 40. D388 | C16 | semidirect |
| 42. C22×C97 | C2×C16 | semidirect |
| 45. C2×D97 | C2×C16 | semidirect |
| 51. C4×C97 | C2×C16 | semidirect |
| 52. Dic97 | C2×C16 | semidirect |
| 59. C97 | D4×C16 | semidirect |
| 90. D4 | #13095525 | direct (N × H) |
| 105. C22 | C2×#13095525 | semidirect |
| 111. C4 | C2×#13095525 | semidirect |
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 |
| C22⋊#13095525 | 2 |
| C4×#13095525 | 2 |
| D4×#11715906 | 2 |
| D4×C16 | 97 |