Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
774 conjugacy classes of subgroups; only the 297 normal subgroups are shown.
This group has 774 conjugacy classes of subgroups — too many to draw. Only its 297 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. C2×#20263333 | C2 | semidirect |
| 2. #27161046 | C2 | semidirect |
| 3. #27161043 | C2 | semidirect |
| 4. C2×C22⋊#13096802 | C2 | semidirect |
| 7. C2×#15691342 | C22 | semidirect |
| 8. C22×#13096802 | C22 | semidirect |
| 11. C22⋊#13096802 | C22 | semidirect |
| 12. C22⋊#13096802 | C22 | semidirect |
| 76. C22×C197 | #131 | semidirect |
| 88. C197 | #2880 | semidirect |
| 165. C22 | #20263333 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263333 | 2 |
| #27161046 | 2 |
| #27161043 | 2 |
| C2×C22⋊#13096802 | 2 |
| C22×#41×C197 | 2 |
| #2880 | 197 |