Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
420 conjugacy classes of subgroups; only the 130 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 130 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. #15690889 | C4 | semidirect |
| 12. C2×#13095490 | C4 | semidirect |
| 14. C2×C4×Dic97 | C4 | semidirect |
| 15. C2×C42×C97 | C4 | semidirect |
| 83. C97 | #1740 | semidirect |
| 98. C2×C42 | #87604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690889 | 2 |
| #20261613 | 2 |
| C2×#15690767 | 2 |
| #1740 | 97 |