Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
852 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 852 conjugacy classes of subgroups — too many to draw. Only its 153 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 |
|---|---|---|
| 2. C2×C22⋊#13096802 | C2 | semidirect |
| 3. C2×#20263238 | C2 | semidirect |
| 4. C2×C22⋊C8×C197 | C2 | semidirect |
| 12. C22×#13096802 | C22 | semidirect |
| 16. C22×C8×C197 | C22 | semidirect |
| 22. C23×D197 | C8 | semidirect |
| 84. C22×C197 | C22⋊C8 | semidirect |
| 97. C2×D197 | C22⋊C8 | semidirect |
| 109. C197 | #1779 | semidirect |
| 114. C2×C22⋊C8 | D197 | semidirect |
| 124. C22×C8 | C2×D197 | semidirect |
| 202. C22 | #20263238 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C4×D197 | 2 |
| C2×C22⋊#13096802 | 2 |
| C2×#20263238 | 2 |
| C2×C22⋊C8×C197 | 2 |
| #1779 | 197 |