Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
656 conjugacy classes of subgroups; only the 245 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 245 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. #27160948 | C2 | semidirect |
| 4. #27160945 | C2 | semidirect |
| 6. #27160930 | C2 | semidirect |
| 7. #382×C197 | C2 | semidirect |
| 17. C42×D197 | C4 | semidirect |
| 54. C4×D197 | C4⋊C4 | semidirect |
| 76. Dic197 | #117 | semidirect |
| 82. C197 | #2285 | semidirect |
| 88. #382 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263284 | 2 |
| C2×C42×D197 | 2 |
| #27160948 | 2 |
| #27160945 | 2 |
| #27160938 | 2 |
| #27160930 | 2 |
| #382×C197 | 2 |
| #2285 | 197 |