Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
144 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 89 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. #20260558 | C2 | semidirect |
| 12. M32×C97 | C4 | semidirect |
| 14. C2×C16×C97 | C4 | semidirect |
| 56. C97 | #2155 | semidirect |
| 64. M32 | Dic97 | semidirect |
| 66. C2×C16 | Dic97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690746 | 2 |
| #20260773 | 2 |
| #20260558 | 2 |
| C2×M32×C97 | 2 |
| #2155 | 97 |