Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
294 conjugacy classes of subgroups; only the 34 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 34 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 |
|---|---|---|
| 1. #20261578 | C2 | semidirect |
| 14. C23×D97 | C8 | semidirect |
| 72. C97 | #1316 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261578 | 2 |
| #20260590 | 2 |
| #1316 | 97 |