Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
152 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 63 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 |
|---|---|---|
| 48. #13096802 | Q16 | semidirect |
| 71. C197 | #1591 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161210 | 2 |
| #27161206 | 2 |
| C4×#15691348 | 2 |
| #27160831 | 2 |
| #27160811 | 2 |
| C8×#13096802 | 2 |
| Q8⋊C8×C197 | 2 |
| #1591 | 197 |