Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
740 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 740 conjugacy classes of subgroups — too many to draw. Only its 205 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×C4×D788 | C2 | semidirect |
| 3. #27160982 | C2 | semidirect |
| 4. #27160980 | C2 | semidirect |
| 5. #27160958 | C2 | semidirect |
| 6. #27160955 | C2 | semidirect |
| 7. #27160944 | C2 | semidirect |
| 8. #27160925 | C2 | semidirect |
| 9. C2×C4×D4×C197 | C2 | semidirect |
| 13. #20263322 | C4 | semidirect |
| 33. C2×D788 | C2×C4 | semidirect |
| 36. C2×C22⋊D197 | C2×C4 | semidirect |
| 47. C4×Dic197 | C2×C4 | semidirect |
| 51. C2×D4×C197 | C2×C4 | semidirect |
| 60. C42×C197 | D4 | semidirect |
| 123. C197 | #2328 | semidirect |
| 127. C2×C4×D4 | D197 | semidirect |
| 164. C2×D4 | C4×D197 | semidirect |
| 184. C42 | C22⋊D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263322 | 2 |
| C2×C4×D788 | 2 |
| #27160982 | 2 |
| #27160980 | 2 |
| #27160958 | 2 |
| #27160955 | 2 |
| #27160944 | 2 |
| #27160925 | 2 |
| C2×C4×D4×C197 | 2 |
| #2328 | 197 |