Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
160 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 78 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. #20261626 | C2 | semidirect |
| 4. #20261625 | C2 | semidirect |
| 8. #15690885 | C4 | semidirect |
| 11. C2×#13095514 | C4 | semidirect |
| 15. #15690750 | C4 | semidirect |
| 17. C16×D97 | C4 | semidirect |
| 18. M32×C97 | C4 | semidirect |
| 63. C97 | #2110 | semidirect |
| 77. M32 | #87604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690885 | 2 |
| #20261698 | 2 |
| #20261626 | 2 |
| #20261625 | 2 |
| M32×D97 | 2 |
| #2110 | 97 |