Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
216 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 119 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. #20261828 | C2 | direct (N × H) |
| 4. #15690905 | C4 | semidirect |
| 6. C2×#13095523 | C4 | semidirect |
| 12. #13095523 | C2×C4 | semidirect |
| 26. C2×#87604 | C16 | semidirect |
| 42. #87604 | C2×C16 | semidirect |
| 47. C2×C97 | C4×C16 | semidirect |
| 49. D97 | C4×C16 | semidirect |
| 52. C97 | C2×C4×C16 | semidirect |
| 101. C2 | #20261828 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690905 | 2 |
| #20261828 | 2 |
| C2×C8×#87604 | 2 |
| C2×C4×C16 | 97 |