Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
248 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 10. #15690744 | C4 | semidirect |
| 54. C8×C97 | C4⋊C4 | semidirect |
| 78. C97 | #1942 | semidirect |
| 132. C8 | #13095490 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690744 | 2 |
| #20260633 | 2 |
| #20260498 | 2 |
| C2×C4×C8×C97 | 2 |
| #1942 | 97 |