Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
404 conjugacy classes of subgroups; only the 130 normal subgroups are shown.
This group has 404 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 |
|---|---|---|
| 3. #20261605 | C2 | semidirect |
| 7. D97⋊M16 | C4 | semidirect |
| 11. #15690889 | C4 | semidirect |
| 18. #15690768 | C4 | semidirect |
| 20. C2×C4⋊Dic97 | C4 | semidirect |
| 23. C2×C4⋊C4×C97 | C4 | semidirect |
| 26. #13095521 | C2×C4 | semidirect |
| 33. C4×#87604 | C2×C4 | semidirect |
| 118. C97 | #1733 | semidirect |
| 137. C2×C4⋊C4 | #87604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D97⋊M16 | 2 |
| C2×#15690889 | 2 |
| #20261605 | 2 |
| C2×#15690768 | 2 |
| #1733 | 97 |