Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
880 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 880 conjugacy classes of subgroups — too many to draw. Only its 229 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×#20263283 | C2 | semidirect |
| 3. C2×C4⋊C4×D197 | C2 | semidirect |
| 4. #27160986 | C2 | semidirect |
| 5. #27160981 | C2 | semidirect |
| 6. #27160980 | C2 | semidirect |
| 7. #27160957 | C2 | semidirect |
| 8. #27160938 | C2 | semidirect |
| 9. #391×C197 | C2 | semidirect |
| 12. C2×#15691359 | C4 | semidirect |
| 40. C2×D788 | C2×C4 | semidirect |
| 49. C2×C4×D197 | C2×C4 | semidirect |
| 61. C2×Q8×C197 | C2×C4 | semidirect |
| 90. C4×D197 | C22⋊C4 | semidirect |
| 133. C197 | #2311 | semidirect |
| 139. #391 | D197 | semidirect |
| 171. C2×Q8 | C4×D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15691359 | 2 |
| C2×#20263283 | 2 |
| C2×C4⋊C4×D197 | 2 |
| #27160986 | 2 |
| #27160981 | 2 |
| #27160980 | 2 |
| #27160957 | 2 |
| #27160938 | 2 |
| #391×C197 | 2 |
| #2311 | 197 |