Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
170 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 47 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×#20263267 | C2 | semidirect |
| 2. C2×#20263265 | C2 | semidirect |
| 3. #27161316 | C2 | semidirect |
| 4. #27161312 | C2 | semidirect |
| 5. #27160906 | C2 | semidirect |
| 6. #27160881 | C2 | semidirect |
| 7. #357×C197 | C2 | semidirect |
| 33. #15691333 | D4 | semidirect |
| 79. C197 | #2218 | semidirect |
| 87. #357 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263267 | 2 |
| C2×#20263265 | 2 |
| #27161316 | 2 |
| #27161312 | 2 |
| #27160906 | 2 |
| #27160881 | 2 |
| #357×C197 | 2 |
| #2218 | 197 |