Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
360 conjugacy classes of subgroups; only the 190 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 190 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 |
|---|---|---|
| 5. #15690865 | C4 | direct (N × H) |
| 6. C4×#11715897 | C4 | semidirect |
| 38. #11715897 | C42 | semidirect |
| 45. C4×C97 | #97 | semidirect |
| 47. Dic97 | #97 | semidirect |
| 55. C97 | C4×#97 | semidirect |
| 103. C4 | #15690865 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690865 | 2 |
| C2×C4×#11715897 | 2 |
| C42×Dic97 | 2 |
| C4×#97 | 97 |