Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
152 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 77 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 |
|---|---|---|
| 17. C2×#11715895 | C8 | semidirect |
| 57. C97 | #1281 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20260788 | 2 |
| C2×#15690721 | 2 |
| #431×C97 | 2 |
| #1281 | 97 |