Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
872 conjugacy classes of subgroups; only the 233 normal subgroups are shown.
This group has 872 conjugacy classes of subgroups — too many to draw. Only its 233 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×#20263291 | C2 | semidirect |
| 3. #27160980 | C2 | semidirect |
| 4. #27160979 | C2 | semidirect |
| 5. #27160938 | C2 | semidirect |
| 6. C4×C22⋊Dic197 | C2 | semidirect |
| 7. #27160926 | C2 | semidirect |
| 8. #380×C197 | C2 | semidirect |
| 10. C2×#15691358 | C4 | semidirect |
| 60. Dic394 | C22⋊C4 | semidirect |
| 70. C2×Dic197 | #41 | semidirect |
| 114. C197 | #2341 | semidirect |
| 121. #380 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15691358 | 2 |
| C2×#20263291 | 2 |
| #27160980 | 2 |
| #27160979 | 2 |
| #27160938 | 2 |
| C4×C22⋊Dic197 | 2 |
| #27160926 | 2 |
| #380×C197 | 2 |
| #2341 | 197 |