Finite Group DatabasebetaFinite Group DatabasebetaOrder 25472.
324 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 89 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. #27164035 | C2 | semidirect |
| 3. #27164024 | C2 | semidirect |
| 4. C2×#20263871 | C2 | semidirect |
| 5. #27163790 | C2 | semidirect |
| 6. C199⋊#338 | C2 | semidirect |
| 7. #568×C199 | C2 | semidirect |
| 11. C2×#15691873 | C4 | semidirect |
| 12. C2×#15691871 | C4 | semidirect |
| 112. C199 | #1903 | semidirect |
| 115. #568 | D199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263980 | 2 |
| #27164035 | 2 |
| #27164024 | 2 |
| C2×#20263871 | 2 |
| #27163790 | 2 |
| C199⋊#338 | 2 |
| #568×C199 | 2 |
| #1903 | 199 |