Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
300 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 66 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 |
|---|---|---|
| 8. C2×#13095490 | C4 | semidirect |
| 10. C2×C4×Dic97 | C4 | semidirect |
| 11. C2×C42×C97 | C4 | semidirect |
| 56. C97 | #1820 | semidirect |
| 66. C2×C42 | #87604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261678 | 2 |
| #20261613 | 2 |
| C2×#15690767 | 2 |
| #1820 | 97 |