Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
272 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 21. #20263244 | C4 | semidirect |
| 104. C197 | #1857 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161556 | 2 |
| #27161122 | 2 |
| #27161121 | 2 |
| C2×#20263244 | 2 |
| #27160985 | 2 |
| #27160839 | 2 |
| #339×C197 | 2 |
| #1857 | 197 |