Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
936 conjugacy classes of subgroups; only the 277 normal subgroups are shown.
This group has 936 conjugacy classes of subgroups — too many to draw. Only its 277 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. C22×C4×Dic197 | C2 | semidirect |
| 3. #27160984 | C2 | semidirect |
| 4. #27160980 | C2 | semidirect |
| 5. #27160956 | C2 | semidirect |
| 6. C4×#15691335 | C2 | semidirect |
| 7. C2×#117×C197 | C2 | semidirect |
| 10. C2×#15691358 | C4 | semidirect |
| 30. C2×Dic394 | C2×C4 | semidirect |
| 33. C2×D788 | C2×C4 | semidirect |
| 43. C2×C4×D197 | C2×C4 | semidirect |
| 70. C2×Dic197 | #41 | semidirect |
| 79. C2×C4×C197 | C22⋊C4 | semidirect |
| 109. C197 | #2297 | semidirect |
| 112. C2×#117 | D197 | semidirect |
| 189. C2×C4 | #15691335 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15691358 | 2 |
| C22×C4×Dic197 | 2 |
| #27160984 | 2 |
| #27160980 | 2 |
| #27160956 | 2 |
| C4×#15691335 | 2 |
| C2×#117×C197 | 2 |
| #2297 | 197 |