Finite Group DatabasebetaFinite Group DatabasebetaOrder 25472.
212 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 73 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. #27163759 | C2 | semidirect |
| 72. C199 | #1528 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263947 | 2 |
| #27164075 | 2 |
| #27163759 | 2 |
| C4×M16×C199 | 2 |
| #1528 | 199 |