Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
476 conjugacy classes of subgroups; only the 253 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 253 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. #27161122 | C2 | semidirect |
| 4. #27161119 | C2 | semidirect |
| 5. #27161115 | C2 | semidirect |
| 6. C2×#20263259 | C2 | semidirect |
| 8. #20263333 | C4 | semidirect |
| 26. #15691342 | C2×C4 | semidirect |
| 27. C2×#13096802 | C2×C4 | semidirect |
| 76. C197 | #2913 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263333 | 2 |
| #27161562 | 2 |
| #27161122 | 2 |
| #27161119 | 2 |
| #27161115 | 2 |
| C2×#20263259 | 2 |
| #520×C197 | 2 |
| #2913 | 197 |