Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
156 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 156 conjugacy classes of subgroups — too many to draw. Only its 93 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. #20260563 | C2 | semidirect |
| 4. #20260561 | C2 | semidirect |
| 14. M32×C97 | C4 | semidirect |
| 28. C16×C97 | C2×C4 | semidirect |
| 56. C97 | #2159 | semidirect |
| 65. M32 | Dic97 | semidirect |
| 84. C16 | C2×Dic97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20260773 | 2 |
| C2×#15690744 | 2 |
| #20260563 | 2 |
| #20260561 | 2 |
| C2×M32×C97 | 2 |
| #2159 | 97 |