Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
256 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 63 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. #27161133 | C2 | semidirect |
| 3. #27161129 | C2 | semidirect |
| 4. #27160803 | C2 | semidirect |
| 5. #27160802 | C2 | semidirect |
| 6. #27160802 | C2 | semidirect |
| 7. #323×C197 | C2 | semidirect |
| 119. C197 | #1469 | semidirect |
| 127. #323 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263312 | 2 |
| #27161133 | 2 |
| #27161129 | 2 |
| #27160803 | 2 |
| #27160802 | 2 |
| #323×C197 | 2 |
| #1469 | 197 |